Basic Analysis I — Real Analysis · Problem 5.3.13

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · riemann-sums-limits

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}}