Convergence tests for series from "summary" of Differential Calculus by S Balachandra Rao
Convergence tests are used to determine whether a given series converges or diverges. One such test is the comparison test, which states that if the terms of a series are all positive and can be shown to be smaller than the terms of a convergent series, then the original series must also converge. Another important test is the ratio test, which involves taking the limit of the ratio of consecutive terms in a series. If this limit is less than 1, then the series converges; if it is greater than 1, the series diverges; and if it is equal to 1, the test is inconclusive. The root test is similar to the ratio test, but involves taking the nth root of the absolute value of the terms in a series. If this limit is less than 1, then the ser...
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