Question

Determine whether the following series converges. 00 Σ 6-1 *2k/ Ink) Leta 20 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. The series converges because ak 6 k(Ink) Is nonincreasing in magnitude for k greater than some Index N and lim ax - k-00 and for any index N, there are some values of k> N for which ak +12 a, and some values of > N for which ax +1 Sak OB. The series diverges because a OC. The series converges because a - OD. The series diverges because ax - and for any index N there are some values of k> N for which ax+12, and some values of k>N for which ak+1 Sa is nondecreasing in magnitude for k greater than some index N. is nondecreasing in magnitude for k greater than some index N. is nonincreasing in magnitude for k greater than some index N and lim - O E. The series converges because ax OF. The series diverges because k-00

Answer 1

E ار۱ is positive and Thank you! 6(-1) 2=2 E cences) G. E k=2 kilncent A Apply teamarting monolone decorating Sesies test an lim an = 0 7-700 acca ac pla(ko) is tive and and monotone from N=2 asing Therefore positive decarea lim kys0 Ilocico) lim [Linck) ها lim K-200 lim (k ln(er)) 1-00 - 6 test the alteanating Serie BO Converges