Show that the series diverges:

SUMMATION from k=0 to infinity of [(k+1)/k]^k

All help is greatly appreciated!!

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- Apr 30th 2008, 12:34 AMjgallShow that a series diverges. Please Help ASAP!
Show that the series diverges:

SUMMATION from k=0 to infinity of [(k+1)/k]^k

All help is greatly appreciated!! - Apr 30th 2008, 12:37 AMIsomorphism

$\displaystyle \lim_{k \to \infty} a_k = \lim_{k \to \infty} \left(1 + \frac1{k}\right)^k = e \neq 0$

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 $\displaystyle \lim_{k \to \infty} a_k \neq 0$