Telescoping Series

#Calc-2#Math#Series A telescoping series is a Series whose general term can be written as the difference of two consecutive terms in a sequence.

For example, $\sum _{k=1}^{\infty }\frac{1}{k(k+1)}=\sum _{k=1}^{\infty }\frac{1}{k+1}-\frac{1}{k+2}$ (after partial fraction expansion)

The partial sums of telescoping series only consist of two terms after cancellation.

good example I didnt really take much notes on this so im kind at a loss