Problem
ALG-B1-M05-P003 Simplest Telescoping
#3
★☆☆☆☆ Level 1 of 5
Find \(\frac1{1\cdot2}+\frac1{2\cdot3}+\cdots+\frac1{10\cdot11}\).
Decompose \(\frac1{k(k+1)}\).
\(\frac1{k(k+1)}=\frac1k-\frac1{k+1}\). The sum is \(1-\frac1{11}=\frac{10}{11}\).
Classic telescoping example.