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SECTION 8.4 OTHER CONVERGENCE TESTS 591 www.stewartcalculus.com Note: Although the Ratio Test works in Example 9. another method is to use the Test We now have several tests for convergence for Divergence. Since of series. So, given a series, how do you know which test to use? For advice, click on non. n . . . .'n. Additional Topics and then on Strategy for n! 1 . 2 . 3 . . . . .n Testing Series. it follows that a, does not approach 0 as n - co. Therefore the given series is divergent by the Test for Divergence. 8.4 Exercises 1. (a) What is an alternating series? 13. For what values of p is the following series convergent? (b) Under what conditions does an alternating series converge? (1)" (c) If these conditions are satisfied, what can you say about the remainder after n terms? 14-16 Show that the series is convergent. How many terms of the 2. What can you say about the series E a, in each of the follow- series do we need to add in order to find the sum to the indicated ing cases? accuracy? (a) lim - 0.8 (-1)' (b) lim an 14. P n 5" (| error |