Lebl-Basic-Analysis-I · Problem 5.3.13

The Riemann Integral

Mathematics · riemann-sums

Problem

For any

\ell \in \mathbb{N}

, show that the following limit exists and find what it is:

\lim_{n\to\infty} \sum_{k=1}^n \frac{k^\ell}{n^{\ell+1}}