Basic Analysis I — Real Analysis · Problem 5.5.3

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · improper-integrals-integral-test

Problem

a) Estimate

\sum_{n=1}^{\infty} \frac{1}{n(n+1)}

correct to within

0.01

using the integral test. b) Compute the limit of the series exactly and compare. Hint: The sum telescopes.