prove $\lim_{n→∞}\left(\frac{∑^{n}_{k=1}k^{m}}{n^{m+1}}\right)=1/(m+1)$ I'm having trouble proving the following equation:
$$\lim_{n→∞}\left(\frac{∑^{n}_{k=1}k^{m}}{n^{m+1}}\right)=\frac{1}{(m+1)}$$
A link to a proof would suffice.
Thank you.

Hint: Regard the expression as a limit of a Riemann sum, and evaluate the (easy) corresponding integral.
