Show that the series diverges:
SUMMATION from k=0 to infinity of [(k+1)/k]^k
All help is greatly appreciated!!
$\displaystyle \lim_{k \to \infty} a_k = \lim_{k \to \infty} \left(1 + \frac1{k}\right)^k = e \neq 0$
If a series $\displaystyle \sum_{k \in \mathbb{N}} a_k $ is convergent then $\displaystyle a_k \to 0$ as $\displaystyle k \to \infty$, but here $\displaystyle \lim_{k \to \infty} a_k \neq 0$