Telescoping

Lesson · Intermediate

Algebra: Sequences & Series

\frac1{1\cdot2} +\frac1{2\cdot3} +\cdots +\frac1{n(n+1)} = 1-\frac1{n+1}

\frac{2^3-1}{2^3+1} \cdot \frac{3^3-1}{3^3+1} \cdots \frac{n^3-1}{n^3+1} = \frac{2(n^2+n+1)}{3n(n+1)}

\frac1{1\cdot2} +\frac1{2\cdot3} +\cdots +\frac1{n(n+1)} = 1-\frac1{n+1}