How to find limit of sum $\lim\limits_{n\to\infty}\sum_{k=1}^{100n}\frac{k^p}{n^{p+1}}$ How can I find this limit? I've tried to use Stolz theorem, but have not succeed. I have heard smth about Riemann sums, but have not found good algorithm how to use it. Can you help me to solve it with the help of riemann sums or show me algorithm how to use it

Hint:
$$\lim_{n\to \infty}\dfrac{1}{n}\sum_{k=1}^{100n}\left(\dfrac{k}{n}\right)^p=\int_{0}^{100}x^p\mathrm dx$$

For the general case: $$\lim_{n\to \infty}\dfrac{1}{n}\sum_{k=0}^{\alpha n}f\left(\dfrac{k}{n}\right)=\int_{0}^{\alpha}f(x)\mathrm dx \ , \ \lim_{n\to \infty} \dfrac{k}{n}\Biggl|_{k=\alpha n}=\alpha $$
