11. Use the alternating series test to determine whether the series is is convergent or divergent. 1- 1/4 + 1/9 1/16 + .. .

20. Find the sum, if it exists, of the infinite geometric series S = 1+++ +.... S = 3 OS = 2 The series diverges. OS= 4 FULL HD 1080 esc %24 % & 4 tab W e

4.-Determine if the following series converges or diverges

5. Consider the series n! n=0 for real numbers x. (a) Use the ratio test to determine the values x for which the series is absolutely convergent. (b) Does this mean that the series is convergent for these values of x? Explain. (c) Explain how one can use part (b) above to determine the limit of the sequence {an} where 22n an n!