For each sequence a, find a number k such that nkan has a finite non-zero limit. (This is of use, because by the limit comparison test the series a, and n-k both converge or both Σ Σ n=1 n=1 diverge.) : (4 + 2n)-2 A. An %3D B. an = n°+n k = 2n2+2n+2 6n°+6n+2 C. an k = 2n2+2n+4 D. an Gnº+6n+2ñ ) %3!

Uk 7. Suppose that the series uk converges, and Ev diverges. Show that Σ(uk + vk) and Σ(ukvk) both diverge.

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Consider the series Sk = n=1 a. Find the general formula for the sum of the first k terms. Your answer should be in terms of k. n=1 4 n² + n b. The sum of a series is defined as the limit of the sequence of partial sums, which means 1)= 4 n² + n = lim k->∞0 c. Select all true statements (there may be more than one correct answer): A. The series is a telescoping series (i.e., it is like a collapsible telescope). B. Most of the terms in each partial sum cancel out. OC. The series is a geometric series. D. The series is a p-series. E. The series converges. 9-