Which of the following infinite series converge? n(n + 2) Σn=1 (n + 3)^4 tan^(-1)(ln n) ln(n - 1) / n (n + 3) Σn=2 √(n) / n a. i only b. ii only c. i and ii only d. i and iii only e. ii and iii only
Added by Kimberly B.
Step 1
Taking the limit of the ratio of consecutive terms, we get: lim n->inf [(n+1)(n+3)^4/n(n+2)] = lim n->inf [(n+1)/(n+2)] * [(n+3)^4/n^4] = 1 * lim n->inf [(1+3/n)^4] = 1 Since the limit is equal to 1, the series does not converge. ii) tan^-1(ln n)/ln(n-1): We Show more…
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