Determine whether the following series converges. k 11k6 +1 Σ (-1)k+1. k=1 Let ak 20 represent the magnitude of the term

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Determine whether the following series converges. k 11k6 +1 Σ (-1)k+1. k=1 Let ak 20 represent the magnitude of the terms of the given series. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The series diverges because for any index N, there are some values of k>N for which ak+ 1 ≥ ak and some values of k> N for which ak + 1 ≤ak- OB. The series diverges because ak is nonincreasing in magnitude for k greater than some index N and lim ak = k→∞o O C. The series converges because ak is nonincreasing in magnitude for k greater than some index N and lim ak = k→∞o O D. The series converges because ak is nondecreasing in magnitude for k greater than some index N. O E. The series diverges because ak is nondecreasing in magnitude for k greater than some index N. O F. The series converges because for any index N, there are some values of k> N for which ak + 12 ak and some values of k> N for which ak+1 ≤ak-