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In mathematics, the ratio test is a test (or "criterion") for the convergence of a series =, where each term is a real or complex number and a n is nonzero when n is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test.
Calculates and displays a ratio at N:1 {{Calculate ratio|5|3}} gives 1.7:1 {{Calculate ratio|5|3|2}} gives 1.67:1 Template parameters [Edit template data] This template prefers inline formatting of parameters. Parameter Description Type Status 1 1 Number being divided Example 5 Number required 2 2 Number being converted to 1 Example 3 Number required 3 3 Number of decimals Default 1 Example 2 ...
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Whether you use Microsoft Office Excel, Google Sheets or Apple Numbers, there’s a free spreadsheet for you. These budgeting templates will give you a head start from simple monthly and yearly ...
English: A plot showing how the ratio test test is proven in the convergent case. Given a sequence like the blue one, for which the ratio of adjacent terms | a n + 1 / a n | {\displaystyle |a_{n+1}/a_{n}|} converges to L < 1, we identify a ratio r = (L+1)/2 and show that for large enough n the sequence is dominated by the simple geometric ...
The likelihood-ratio test, also known as Wilks test, [2] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. [3] In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent.
If the null hypothesis is true, the likelihood ratio test, the Wald test, and the Score test are asymptotically equivalent tests of hypotheses. [8] [9] When testing nested models, the statistics for each test then converge to a Chi-squared distribution with degrees of freedom equal to the difference in degrees of freedom in the two models.