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Unformatted text preview: (12.7) Strategy for Convergence Tests To test series for convergence, there are some rough rules of thumb to follow to decide which convergence tests to apply. • Perhaps the first thing to consider for a series ∑ a n is whether lim n →∞ a n = 0. If that isn’t true, the series cannot converge. • If the series is alternating, try the alternating series test. • If a n has roots and powers of n in it (e.g., ∑ √ n n 3 +1 ), a comparison test with a p-series is probably in order. (In this case, compare with ∑ 1 n 5 / 2 .) • If a n has exponents or factorials in it, the ratio test is probably the one to try. • Occasionally, the root test is good to try, if a n consists of something raised to the n-th power, such as a n = 2 n 3 n +1 n . • The integral test is not used very often. Occasionally, there will be a series that’s not amenable to the other tests, where the integral test works....
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- Fall '08
- Mathematical Series