Possible Duplicate:
Proving $(1 + 1/n)^{n+1} \gt e$
How to prove this:
$$ \left(\frac{x}{x-1}\right)^x \geq e \qquad\text{for}\qquad x \in \mathbb{N}^* $$
$e$ is the base of the natural logarithm.
and I think the equal satisfies if $x$ converges to infinity.
Thank you!