Evaluating the limit $\lim \limits_{x \to \infty} \frac{x^x}{(x+1)^{x+1}}$ How do you evaluate the limit 
$$\lim_{x \to \infty} \frac{x^x}{(x+1)^{x+1}}?$$

I think we should be witty about how we write it. How about we consider instead the limit $$ \lim_{x \to \infty} \frac{x^x}{(x+1)^x (x+1)} = \lim_{x \to \infty} \left ( \frac{x}{x+1} \right )^{x} * \frac{1}{x+1} $$
I think that this is suggestive of a proof?
