11. Apply the Ordinary Comparison Test to decide whether the following series converge or diverge: a....

 

 

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11. Apply the Ordinary Comparison Test to decide whether the following series converge or diverge: a. n=1 b. C. n=1 n=0 IMs Ms Ms Ms Ms M8 cos(1/n) n cos(1/n) n tan-(n) 4" d. e. n=0 n 2" n=0 2/3 f. n=1 n 1/n 1/3 12. Apply the Ordinary Comparison Test and the inequality ln(n) < nk for any positive number k, if n is big enough (when appropriate to do so), to decide whether or not the following infinite series converge or diverge. Choose an appropriate value for k. a. n=2 In(n) In(n) b. 3/2 n=2 00 c. n=2 00 d. n=2 n 1 n1/2. In(n) [In(n)] n [In(n)] 4/3 e. n=2 00 f. n=2 n n 1 3/4 . [ln(n)] Hint/Warning: the next two problems are different. Use instead the inequality: In(n) In(2) if n 2. 11. Apply the Ordinary Comparison Test to decide whether the following series converge or diverge: a. n=1 b. C. n=1 n=0 IMs Ms Ms Ms Ms M8 cos(1/n) n cos(1/n) n tan-(n) 4" d. e. n=0 n 2" n=0 2/3 f. n=1 n 1/n 1/3 12. Apply the Ordinary Comparison Test and the inequality ln(n) < nk for any positive number k, if n is big enough (when appropriate to do so), to decide whether or not the following infinite series converge or diverge. Choose an appropriate value for k. a. n=2 In(n) In(n) b. 3/2 n=2 00 c. n=2 00 d. n=2 n 1 n1/2. In(n) [In(n)] n [In(n)] 4/3 e. n=2 00 f. n=2 n n 1 3/4 . [ln(n)] Hint/Warning: the next two problems are different. Use instead the inequality: In(n) In(2) if n 2.