Expii

# Extension: Infinite Telescoping Series as a Limit - Expii

Just like you can (sometimes) compute integrals by anti-differentiation, you can sometimes compute infinite series by "anti-difference-ing": if you can find a sequence $$(b_n)_{n\ge0}$$ such that $$b_{n+1} - b_n = a_n$$ for all $$n$$, then $$\sum_{n\ge0} a_n = \lim_{n\to\infty} (b_{n+1} - b_0) = -b_0 + \lim_{n\to\infty} b_n$$.
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