For summation questions involving telescopic sums/series. This tag is often used with (summation) or (sequences-and-series).
In mathematics, a telescoping sum $(a_n)_n$ is a series whose general term $a_n$ can be decomposed as the difference between two consecutive terms of another series $(b_n)_n$, so that only a finite number of terms is left in the sum. $$\sum_{i = 1}^N a_n = \sum_{i = 1}^N (b_n - b_{n-1}) = b_N - b_0.$$ In particular, if $\lim\limits_{N \to \infty} b_N \to 0$, $$\sum_{i = 1}^\infty a_n = - b_0.$$
