Mathematics

Mathematics

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

.

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