Determine whether the following series converges. k=0 6(-1) 5k+7 ... Let ak > 0 represent the magnitude of the terms of the given series. Select the correct choice below and fill in the answer box(es) to complete your choice. A. The series diverges because ak = and 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 sak. B. The series diverges because ak = is nonincreasing in magnitude for k greater than some index N and lim ak = k C. The series converges because ak D. The series converges because ak = is nondecreasing in magnitude for k greater than some index N. = is nonincreasing in magnitude for k greater than some index N and lim ak = k E. The series diverges because ak = is nondecreasing in magnitude for k greater than some index N. O F. The series converges because = and 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. Determine whether the following series converges. COS k 2 k=1 k Let ak >0 represent the magnitude of the terms of the given series. Select the correct choice below and fill in the answer box(es) to complete your choice. A. The series diverges because ak = is nondecreasing in magnitude for k greater than some index N. O B. The series converges because ak = and 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 sak C. The series converges because ak = is nondecreasing in magnitude for k greater than some index N. D. The series diverges because ak = is nonincreasing in magnitude for k greater than some index N and lim ak = k- E. 1 The series diverges because ak = k and 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 sak. F. The series converges because ak = is nonincreasing in magnitude for k greater than some index N and limak = k Evaluate the geometric series or state that it diverges. 3" n=04 +1 Does the series converge or diverge? If it converges, what is its sum? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series converges. Its sum is . (Type an integer or a simplified fraction.) B. The series diverges.