# Show that a series diverges. Please Help ASAP!

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• April 30th 2008, 01:34 AM
jgall
Show 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!!
• April 30th 2008, 01:37 AM
Isomorphism
Quote:

Originally Posted by jgall
Show that the series diverges:

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

All help is greatly appreciated!!

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

If a series $\sum_{k \in \mathbb{N}} a_k$ is convergent then $a_k \to 0$ as $k \to \infty$, but here $\lim_{k \to \infty} a_k \neq 0$