Abstract Algebra: Theory and Applications · Problem 2.4.10

Groups — Thomas Judson

Mathematics — Abstract Algebra · induction-telescoping-sum

Problem

Prove that

\frac{1}{2} + \frac{1}{6} + \cdots + \frac{1}{n(n+1)} = \frac{n}{n+1}

for

n \in \mathbb{N}