We would like to show you a description here but the site won’t allow us.Acid-Test Ratio: The acid-test ratio is a strong indicator of whether a firm has sufficient short-term assets to cover its immediate liabilities. This metric is more robust than the current ratio ...transformers, test-procedures. TestGuy June 26, 2016, 4:00am 1. Introduction to Transformer Turns Ratio Testing 897×550 93.2 KB. The transformer turns ratio test is used to determine the number of turns in one winding of a transformer in relation to the number of turns in the other windings of the same phase of the transformer.Abstract. The branch-site test is a likelihood ratio test to detect positive selection along prespecified lineages on a phylogeny that affects only a subset of codons in a protein-coding gene, with positive selection indicated by accelerated nonsynonymous substitutions (with ω = d N /d S > 1). This test may have more power than earlier …이게 사교육의 폐해인가.. 싶기도 합니다. 지난 번에 교대급수 판정법에 대해 포스팅했는데, 정의를 익히고 그대로 문제에 적용하면 된다고 했는데요, 급수의 수렴/발산 문제는 다 그런 식으로 풀어주시면 됩니다 :) Ratio Test는 급수의 수렴/발산을 판정하는 여러 ... lrtest is intended to be a generic function for comparisons of models via asymptotic likelihood ratio tests. The default method consecutively compares the fitted model object object with the models passed in … . Instead of passing the fitted model objects in …, several other specifications are possible. The updating mechanism is the same as ...ダランベールの収束判定法（ダランベールのしゅうそくはんていほう、ratio test）とは、実数や複素数を項にもつ級数が、収束するか発散するかを判定する方法である。級数における、前後の項の比を考える。 Jul 6, 2018 · An alternating series is one in which the terms alternate sign, so positive, then negative, then positive, etc. How can we generate a series like this, and h... The prothrombin time test also may be performed to check for liver disease. It is one of many tests used to screen people waiting for liver transplants. That screening — known as the model for end-stage liver disease (MELD) — is a scoring system for assessing the severity of chronic liver disease. If your provider suspects you have …Ratio test (Sect. 10.5) I The ratio test. I Using the ratio test. I Few more examples. I Comment: The root test. The ratio test Remark: The ratio test is a way to determine …An A/G ratio test measures albumin and globulin, the two main proteins in your blood. This simple blood test is used to monitor your nutritional status, immune function, and overall health. High ...The Ratio Test tests a series for convergence or divergence by considering the limit of successive terms. It is an important test: For example, it’s frequently used in finding the interval of convergence of power series. Theorem. (Ratio Test) Let X∞ k=1 a k be a series with positive terms. Let L = lim k→∞ a k+1 a k. (a) If L < 1, the ... Online test for face beauty analysis. Analyze your face in 3 minutes. Rate my face 1-100. How beautiful am I? Are you pretty? Ask us with confidentiality. Upload photo or use webcam. Please do not start if you have low self-esteem or confidence issues.Infinite Series: Ratio Test For Convergence. The ratio test may be used to test for convergence of an infinite series. Related Topics: Integral Test. Comparison Test. Root Test.The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald [1] and later proven to be optimal by Wald and Jacob Wolfowitz. [2] Neyman and Pearson's 1933 result inspired Wald to reformulate it as a sequential analysis problem. The Neyman-Pearson lemma, by contrast, offers a rule of …Regarding colors, the standard defines two levels of contrast ratio: AA (minimum contrast) and AAA (enhanced contrast). The level AA requires a contrast ratio of at least 4.5:1 for normal text and 3:1 for large text (at least 18pt) or bold text. The level AAA requires a contrast ratio of at least 7:1 for normal text and 4.5:1 for large text or ...The ratio test may be used to test convergence by comparing to a geometric series. If the absolute value of the ratio of successive terms in the sequence is less than 1, the series converges. If this ratio is larger than 1, the series diverges. d'Alembert's test: Also known simply as the ratio test. Attributed to Jean-Baptiste le Rond d'Alembert, it is a criterion for the convergence of a series, ...The objective of this test is to monitor the athlete's waist-to-hip ratio, which is related to the risk of coronary heart disease - Han (1995) and Dobbelsteyn (2001). Required Resources To conduct this test, you will require:A free online tool to check the convergence of series using the ratio test. Enter a series expression and get the result, along with the step-by-step solution and the graph of the …Winding Resistance Test; Burden Test; 1. Ratio Test. The CT ratio is defined as the relationship between the primary current input and the secondary current output at full load. For instance, a CT with a ratio of 300:5 will generate 5 amps of secondary current when 300 amps flow through the primary side. (300:5 = 60:1)About urine albumin-creatinine ratio (uACR) The urine albumin-creatinine ratio (uACR) test measures the amount of two different substances in your urine - albumin (a protein) and creatinine. Albumin is an important protein normally found in the blood that serves many roles in the body. These roles include building muscle, repairing tissue, and ...9.6E: Exercises for Ratio and Root Tests. In exercises 1 - 11, use the ratio test to determine whether each series ∞ ∑ n = 1an converges or diverges. State if the ratio test is …This is exactly how one finds the common ratio in a geometric sequence ( r = an+1 an) r = a n + 1 a n). We then take the limit of this ratio, which I assume is to find the relative rate of change between an+1 a n + 1 and an a n. In which case, it is more effective to take the absolute value of the limit, limn→∞∣∣ an+1 an ∣∣ = L lim ...The sequential approach also allows for an indeterminate outcome, so if A < Λ 1 < B, continue sampling and go to Step 2. Step 2: Observe X 2. Compute the probability ratio Λ 2 = f 1 ( x 1, x 2) ∕ f 0 ( x 1, x 2 ). As in Step 1, if Λ 2 ≥ B, reject H 0, while if Λ 2 ≤ A, accept H 0. If A < Λ 2 < B, continue sampling and observe X 3.Cauchyの収束条件からダランベールの収束判定法（ratio test）まで証明を行い,実際に例題を解いて使い方を解説します. 本稿では級数の収束,発散についてまとめました. Cauchyの収束条件からダランベールの収束判定法（ratio test）まで証明を行い,実際 …The ratio test says that, if we have the positive series. ∞ ∑ n = 1an, such that limn → ∞an + 1 an = L, then. (1) if L < 1, then ∑∞n = 1an is absolutely convergent; (2) if L > 1, then ∑∞n = 1an is divergent; (3) if L = 1, then the ratio test gives no information. I want to understand the reasons behind why and how this works ... a) If $R < 1$ then $\displaystyle{\sum_{n=1}^{\infty} a_n}$ converges. b) If $1 < r$ then $\displaystyle{\sum_{n=1}^{\infty} a_n}$ diverges. c) If $r \leq 1 \ ...The likelihood ratio test computes \chi^2 and rejects the assumption if \chi^2 is larger than a Chi-Square percentile with k degrees of freedom, where the ...The likelihood ratio test computes \chi^2 and rejects the assumption if \chi^2 is larger than a Chi-Square percentile with k degrees of freedom, where the ...7.33M subscribers Subscribe Subscribed 6.8K 644K views 5 years ago New Calculus Video Playlist This calculus 2 video tutorial provides a basic introduction into …The Ratio Test and the Root Test. The Ratio Test and the Root Test. The Ratio Test tests a series for convergence or divergence by considering the limit of successive terms. It is an important test: For example, it's frequently used in finding the interval of convergence of power series. Theorem. ( Ratio Test ) Let be a series with positive terms. The ratio test says that, if we have the positive series. ∞ ∑ n = 1an, such that limn → ∞an + 1 an = L, then. (1) if L < 1, then ∑∞n = 1an is absolutely convergent; (2) if L > 1, then ∑∞n = 1an is divergent; (3) if L = 1, then the ratio test gives no information. I want to understand the reasons behind why and how this works ... The protein-to-creatinine ratio in urine allows doctors to determine how much protein is in urine at a specific moment in time, according to Lab Tests Online. A high ratio implies ...4 Verification of voltage ratio and vector group or phase displacement 41 4.1 References / Standards 42 4.2 Purpose of measurement 42 4.3 General 42 4.4 Measuring the voltage ratio 43 4.5 Test circuit 44 4.6 Measuring procedure 49 4.7 Measuring uncertainty 51 A 4 Appendix 52 A 4.1 Determination and localization of errors 52A BUN/Creatinine ratio is found by dividing the BUN count with the creatinine count. Because the body produces much more BUN than creatinine, the ideal ratio lies somewhere between 10:1 and 20:1. Results that are higher than this range mean there is an excess of BUN in the blood, which could mean your kidneys are not getting the proper blood flow.A geometric series is a sequence of numbers in which the ratio between any two consecutive terms is always the same, and often written in the form: a, ar, ar^2, ar^3, ..., where a is the first term of the series and r is the common ratio (-1 < r < 1).10.6 Integral Test; 10.7 Comparison Test/Limit Comparison Test; 10.8 Alternating Series Test; 10.9 Absolute Convergence; 10.10 Ratio Test; 10.11 Root Test; …5. Divide 880g of food between the cat and the dog in the ratio of 3:5. 550:330. 330:550.Learn how to use the ratio test to decide if a series converges or diverges. The ratio test compares the ratio of the terms of the series to the limit of the function at infinity. See examples, video, and tips from other users. Debt-to-Income Ratio Calculator I believe it does if you have a ton of arrears I do believe they can collect. And attach to your credit report. At least that's what's wrong with mi...Ratio test which is also known as D'Alembert's ratio is used to test for positive terms. Ratio test. Let \ (u_ {1}+u_ {2}+u_ {3}+u_ {4}+u_ {5}+\cdot\cdot\cdot+u_ {n}\) be a series of …The ratio test is particularly useful for series involving the factorial function. Consider \(\sum_{n=0}^\infty 5^n/n!\). $$ \lim_{n\to\infty} {5^{n+1}\over (n+1)!}{n!\over …Examples. For example, ⅘ is a ratio and the proportion statement is 20/25 = ⅘. If we solve this proportional statement, we get: 20/25 = ⅘. 20 x 5 = 25 x 4. 100 = 100. Check: Ratio …Comparing the results of total and free PSA tests can give doctors an idea of how likely it is that a person has prostate cancer. Free PSA ranges can vary, but generally, a higher ratio of free ...Dec 21, 2020 · The ratio test is particularly useful for series whose terms contain factorials or exponential, where the ratio of terms simplifies the expression. The ratio test is convenient because it does not require us to find a comparative series. The drawback is that the test sometimes does not provide any information regarding convergence. Details. Likelihood ratio test checks the difference between -2*logLikelihood of the two models against the change in degrees of freedom using a chi-squared test. It is best applied to a model from 'glm' to test the effect of a factor with more than two levels. The records used in the dataset for both models MUST be the same.7.33M subscribers Subscribe Subscribed 6.8K 644K views 5 years ago New Calculus Video Playlist This calculus 2 video tutorial provides a basic introduction into …7.33M subscribers Subscribe Subscribed 6.8K 644K views 5 years ago New Calculus Video Playlist This calculus 2 video tutorial provides a basic introduction into …Nov 16, 2022 · Section 10.11 : Root Test. For each of the following series determine if the series converges or diverges. ∞ ∑ n=1( 3n +1 4−2n)2n ∑ n = 1 ∞ ( 3 n + 1 4 − 2 n) 2 n Solution. ∞ ∑ n=0 n1−3n 42n ∑ n = 0 ∞ n 1 − 3 n 4 2 n Solution. ∞ ∑ n=4 (−5)1+2n 25n−3 ∑ n = 4 ∞ ( − 5) 1 + 2 n 2 5 n − 3 Solution. Here is a ... THE RATIO TEST. THE RATIO TEST. a. the series converges if < 1 b. the series diverges if > 1 or is infinite c. the test is inconclusive if = 1. EXAMPLE 1: Does the following series converge or diverge? SOLUTION: Since this series has a factorial in it, I am going to use the ratio test. FACT: The ratio test works well with series that include Debt ratio refers to the percentage of debt against a person's assets. There are several ways to measure debt ratio when it comes to managing personal finances. These calculations ...ダランベールの収束判定法（ダランベールのしゅうそくはんていほう、ratio test）とは、実数や複素数を項にもつ級数が、収束するか発散するかを判定する方法である。級数における、前後の項の比を考える。 2 Individual variance ratio tests The VR test is often used (see Cochrane, 1988; Lo and MacKinlay, 1988; Poterba and Summers, 1988; among others) to test the hypothesis that a given time series or its first difference (or return), xt =yt −yt−1, is a collection of i.i.d. observations or that it follows a martingale difference sequence.Interpreting test results. Normal urine elimination is less than 150 mg total protein per day and less than 30 mg albumin daily. The urine total protein to creatinine ratio or UPCR (mg/mg) is normally less than 0.2 for adults. Elevated urine protein levels may be seen temporarily with conditions such as infections, stress, pregnancy, diet, cold ...2 Individual variance ratio tests The VR test is often used (see Cochrane, 1988; Lo and MacKinlay, 1988; Poterba and Summers, 1988; among others) to test the hypothesis that a given time series or its first difference (or return), xt =yt −yt−1, is a collection of i.i.d. observations or that it follows a martingale difference sequence.Nov 16, 2022 · Section 10.11 : Root Test. For each of the following series determine if the series converges or diverges. ∞ ∑ n=1( 3n +1 4−2n)2n ∑ n = 1 ∞ ( 3 n + 1 4 − 2 n) 2 n Solution. ∞ ∑ n=0 n1−3n 42n ∑ n = 0 ∞ n 1 − 3 n 4 2 n Solution. ∞ ∑ n=4 (−5)1+2n 25n−3 ∑ n = 4 ∞ ( − 5) 1 + 2 n 2 5 n − 3 Solution. Here is a ... The test is also known as simply a turns ratio test. A TTR test is performed by a ratio meter (ratio tester). This test validates the transformer design, the transformer nameplate, and the transformer’s fixed transforming abilities throughout its service life. A TTR test should be performed to confirm that the transformer’s de-energized tap ...Jul 6, 2018 · An alternating series is one in which the terms alternate sign, so positive, then negative, then positive, etc. How can we generate a series like this, and h... If you are considering an investment, the cash-flow-based accrual ratio can help you choose a company in which to invest. Cash flow is the money “flowing” in and out of a company. ...In general, an albumin/globulin ratio between 1.1 and 2.5 is considered normal, although this can vary depending on the laboratory performing the test [ 4 ]. Your blood usually contains a little more albumin than globulin, which is why a normal ratio is slightly higher than 1 [ 1 ]. For reference, the total amount of albumin in the blood is ...The likelihood ratio (LR) test is a test of hypothesis in which two different maximum likelihood estimates of a parameter are compared in order to decide ...Results of the BUN test are measured in milligrams per deciliter (mg/dL) in the United States and in millimoles per liter (mmol/L) internationally. In general, around 6 to 24 mg/dL (2.1 to 8.5 mmol/L) is considered normal. But normal ranges may vary, depending on the reference range used by the lab and your age.The ratio test may be used to test for convergence of an infinite series. Related Topics: Integral Test; Comparison Test; Root Test The polarization index test is a 10-minute to 1-minute ratio test of insulation resistance.Similarly, the DAR test is a 60-second to 30-second insulation resistance ratio test. The advantage of the insulation resistance time ratio test is the cancellation of measurement errors caused by temperature.The test uses mass spectrometry to measure the ratio of two forms of amyloid in the blood, and it received a “Breakthrough Device” designation from the FDA in 2019. …Just because the Ratio Test doesn’t tell us anything doesn’t mean we can’t determine if this series converges or diverges. In fact, it’s actually quite simple to do in …The Ratio Test and the Root Test. The Ratio Test and the Root Test. The Ratio Test tests a series for convergence or divergence by considering the limit of successive terms. It is an important test: For example, it's frequently used in finding the interval of convergence of power series. Theorem. ( Ratio Test ) Let be a series with positive terms. Nov 26, 2023 · How To Use The Ratio Test. In general, the idea is to set up the ratio and evaluate it. In detail, you need to determine what is and then build , set up the fraction, combine like terms and then take the limit of each term. Setting up the limit and combining like terms are the easy parts. The challenge comes in taking the limit. Nov 16, 2022 · 10.6 Integral Test; 10.7 Comparison Test/Limit Comparison Test; 10.8 Alternating Series Test; 10.9 Absolute Convergence; 10.10 Ratio Test; 10.11 Root Test; 10.12 Strategy for Series; 10.13 Estimating the Value of a Series; 10.14 Power Series; 10.15 Power Series and Functions; 10.16 Taylor Series; 10.17 Applications of Series; 10.18 Binomial ... In this section, we prove the last two series convergence tests: the ratio test and the root test. These tests are particularly nice because they do not require us to find …The Ratio Test can be used on any series, but unfortunately will not always yield a conclusive answer as to whether a series will converge absolutely or diverge. A proof of the Ratio Test is also given. Root Test – In this section we will discuss using the Root Test to determine if an infinite series converges absolutely or diverges. The Root ...If you are considering an investment, the cash-flow-based accrual ratio can help you choose a company in which to invest. Cash flow is the money “flowing” in and out of a company. ...Nov 21, 2023 · The ratio test states that a series converges if the limit of the ratio of consecutive terms is strictly less than 1. Convergent tests like the ratio test are useful because it is often difficult ... Analyzing financial ratios can provide insight into a company’s strengths, weaknesses, competitive advantages and strategy. While different industries can have wildly different rat...lrtest is intended to be a generic function for comparisons of models via asymptotic likelihood ratio tests. The default method consecutively compares the fitted model object object with the models passed in … . Instead of passing the fitted model objects in …, several other specifications are possible. The updating mechanism is the same as ...Analysis of financial ratios serves two main purposes: 1. Track company performance. Determining individual financial ratios per period and tracking the change in their values over time is done to spot trends that may be developing in a company. For example, an increasing debt-to-asset ratio may indicate that a company is overburdened with debt ...Nov 16, 2022 · 10.6 Integral Test; 10.7 Comparison Test/Limit Comparison Test; 10.8 Alternating Series Test; 10.9 Absolute Convergence; 10.10 Ratio Test; 10.11 Root Test; 10.12 Strategy for Series; 10.13 Estimating the Value of a Series; 10.14 Power Series; 10.15 Power Series and Functions; 10.16 Taylor Series; 10.17 Applications of Series; 10.18 Binomial ... Just because the Ratio Test doesn’t tell us anything doesn’t mean we can’t determine if this series converges or diverges. In fact, it’s actually quite simple to do in …Unit test. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.4. Determine whether the series converges ∞ ∑ k = 1(k!)2 (2k)! Attempt: I used ratio test, but I guess I am making a mistake in cancelling out terms. lim k → ∞((k + 1)!)2 (2(k + 1))!(2k)! (k!)2 = lim k → ∞k + 1 2. I am not experienced with factorials. For example, I know that (k + 1)! = k!(k + 1), but I cant figure what (2(k + 1 ... Profitability ratios help investors, bankers, and entrepreneurs gauge the health and sustainability of their businesses. Trusted by business builders worldwide, the HubSpot Blogs a...The uACR is a simple urine test that's part of a routine exam. Blood or protein in the urine may be a sign of kidney disease. A normal amount of albumin in your urine is less than 30 mg/g. ... They will also do a urine albumin-creatinine ratio (uACR), which shows if you have protein (albumin) in the urine. Protein in the urine may mean you have ...Your test results: A preview Your test results will show your cholesterol levels in milligrams per deciliter of blood, or mg/dL. Total cholesterol and HDL (good) cholesterol are among numerous factors your health care professional can use to predict your lifetime or 10-year risk for a heart attack or stroke.POWERED BY THE WOLFRAM LANGUAGE. ratio test vs root test. ratio test vs constant multiple rule for differentiation. tests. alternating series test. comparison test. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. While a company's stock price reflects the value that investors are placing on that investment, the price-to-earnings ratio, called P/E ratio, illustrates a stock's worth based on ...Nov 16, 2022 · As with the ratio test, if we get \(L = 1\) the root test will tell us nothing and we’ll need to use another test to determine the convergence of the series. Also note that, generally for the series we’ll be dealing with in this class, if \(L = 1\) in the Ratio Test then the Root Test will also give \(L = 1\). The likelihood ratio test (LRT) is a statistical test of the goodness-of-fit between two models. A relatively more complex model is compared to a simpler model to see if it fits a particular dataset significantly better. If so, the additional parameters of the more complex model are often used in subsequent analyses.A doctor can diagnose dehydration when the BUN-to-creatinine ratio is high, reports WebMD. A high BUN-to-creatinine ratio occurs when BUN levels are higher than creatinine levels. ...Nov 16, 2022 · As with the ratio test, if we get \(L = 1\) the root test will tell us nothing and we’ll need to use another test to determine the convergence of the series. Also note that, generally for the series we’ll be dealing with in this class, if \(L = 1\) in the Ratio Test then the Root Test will also give \(L = 1\).
ダランベールの収束判定法（ダランベールのしゅうそくはんていほう、ratio test）とは、実数や複素数を項にもつ級数が、収束するか発散するかを判定する方法である。級数における、前後の項の比を考える。 . Cheap flights to cali
The typical adult range for the BUN-to-creatinine ratio is 1 unit of creatinine for every 10 to 20 units of blood-urea nitrogen, states Lab Tests Online. However, WebMD claims the ...In most cases, you will use the highlighted column (α = .05). The critical value of t for your test is found where the row and column meet. Example: Finding the critical value of t in the t table. Using the t table, you find that for a two-tailed test with df = 29 and α = .05 the critical value of t is 2.045.Testing Under the Normal Distribution. Consider the situation in which X is a collection of normal random variables with unknown mean μ ∈ ℝ and variance σ2 > 0. The parameter space is ( μ , σ2 ) ∈ Θ = ℝ × ℝ +. The densities are of the form f ( x ; μ , σ2 ) = (2 πσ2) −1/2 exp {− ( x − μ) 2 / (2 σ2 )}, so the reduced ...A cholesterol test can measure: total cholesterol – the overall amount of cholesterol in your blood; good cholesterol (called HDL) – this may make you less likely to have heart problems or a stroke; non-HDL cholesterol – the difference between total cholesterol and HDL; When you get your result, you may just be told your total cholesterol.d'Alembert's test: Also known simply as the ratio test. Attributed to Jean-Baptiste le Rond d'Alembert, it is a criterion for the convergence of a series, ...The ratio test compares two consecutive terms of a series to determine if the series converges or diverges. The ratio is L= \lim_ {n\to\infty}\frac {a_ {n+1}} {a_n}. If L1 then the series does not converge, and if L=1 or does not exist, then the test is inconclusive. Your test results: A preview Your test results will show your cholesterol levels in milligrams per deciliter of blood, or mg/dL. Total cholesterol and HDL (good) cholesterol are among numerous factors your health care professional can use to predict your lifetime or 10-year risk for a heart attack or stroke.An A/G ratio test measures albumin and globulin, the two main proteins in your blood. This simple blood test is used to monitor your nutritional status, immune function, and overall health. High ...6th grade 11 units · 148 skills. Unit 1 Ratios. Unit 2 Arithmetic with rational numbers. Unit 3 Rates and percentages. Unit 4 Exponents and order of operations. Unit 5 Negative numbers. Unit 6 Variables & expressions. Unit 7 Equations & inequalities. Proof of Integral Test. First, for the sake of the proof we’ll be working with the series ∞ ∑ n=1an ∑ n = 1 ∞ a n. The original test statement was for a series that started at a general n =k n = k and while the proof can be done for that it will be easier if we assume that the series starts at n =1 n = 1.Winding Resistance Test; Burden Test; 1. Ratio Test. The CT ratio is defined as the relationship between the primary current input and the secondary current output at full load. For instance, a CT with a ratio of 300:5 will generate 5 amps of secondary current when 300 amps flow through the primary side. (300:5 = 60:1)The surface quality of an optical lens can be quantitatively measured using a scatter ratio test. A collimated light beam is focused by the test lens upon ...A BUN/Creatinine ratio is found by dividing the BUN count with the creatinine count. Because the body produces much more BUN than creatinine, the ideal ratio lies somewhere between 10:1 and 20:1. Results that are higher than this range mean there is an excess of BUN in the blood, which could mean your kidneys are not getting the proper blood flow.When it comes to working with mortar, achieving the perfect mix ratio is crucial. The mix ratio determines the strength and durability of the mortar, ensuring that it can withstand...Learn how to use the ratio test to decide if a series converges or diverges. The ratio test compares the ratio of the terms of the series to the limit of the function at infinity. See examples, video, and tips from other users. A similar argument to the one used for the Ratio Test justifies a related test that is occasionally easier to apply, namely the so-called Root Test . Theorem 6.61. Root Test. Given a series ∑an ∑ a n with positive terms and lim n→∞(an)1/n = L: lim n → ∞ ( a n) 1 / n = L: If L< 1, L < 1, then the series converges.Acid-Test Ratio: The acid-test ratio is a strong indicator of whether a firm has sufficient short-term assets to cover its immediate liabilities. This metric is more robust than the current ratio ....