Determine whether the following series converges. DO 2(-n* + 1 Ink K2 k =1 Let ak > 0 represent the magnitude of the terms of the given series. Identify and describe ak- Select the correct choice below and fill in any answer box in your choice. O A. The series converges because ak = and for any index N, there are some values of k > N for which ak + 1 2 ax and some values of k > N for which ak + 1 sak O B. The series diverges because a* = is nondecreasing in magnitude for k greater than some index N. O C. The series diverges because ak = is nonincreasing in magnitude for k greater than some index N and lim ak = k-+00 O D. The series converges because ak = is nonincreasing in magnitude for k greater than some index N and lim ak = K-+00 O E. The series diverges because ak = and for any index N, there are some values of k > N for which ak + 1 2 ax and some values of k > N for which ak + 1 sak- OF. The series converges because ak = is nondecreasing in magnitude for k greater than some index N