Consider the series with

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider the series

\displaystyle \sum_{n=1}^{\infty} \frac{n^{n}}{k^{\,n}\, n!}

with

k>0

. For which values of

k

does the series converge? (a) It converges when

k\ge e

and diverges when

k<e

. (b) It converges when

k>e

and diverges when

k\le e

. (c) It converges when

k>1

and diverges when

k\le 1

. (d) It diverges for all positive

k