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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 isnt 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 thats not amenable to the other tests, where the integral test works....
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- Fall '08