Prove that the sequence $\displaystyle a_n=\frac{n^n}{n!}$ is increasing.

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- Jan 13th 2012, 01:09 PMalexmahoneProve that the sequence is increasing
Prove that the sequence $\displaystyle a_n=\frac{n^n}{n!}$ is increasing.

- Jan 13th 2012, 01:22 PMgirdavRe: Prove that the sequence is increasing
Compute $\displaystyle \frac{a_{n+1}}{a_n}$.

- Jan 13th 2012, 01:23 PMPlatoRe: Prove that the sequence is increasing
- Jan 13th 2012, 01:37 PMalexmahoneRe: Prove that the sequence is increasing
$\displaystyle a_{n+1}=\frac{(n+1)^{n+1}}{(n+1)!}=\frac{(n+1)^n}{ n!}>\frac{n^n}{n!}=a_n$

So, $\displaystyle a_n$ is increasing.