Possible Duplicate:
How to prove $(1+1/x)^x$ is increasing when $x>0$?
Let $k \in \mathbb{N}$ be fixed. For all $n \in \mathbb{N}$, is it true that
$\left(\frac{n-1}{n}\right)^{n-1} \leq \left(\frac{n-k-1}{n-k}\right)^{n-k-1}?$
Maple suggests the inequality holds, but I see no straightforward way to compare these two quantities; the fraction on the left is closer to one but has a higher exponent compared with the righthand side.