Evaluate a sum which almost looks telescoping but not quite – math.stackexchange.com

Evaluate a sum which almost looks telescoping but not quite – math.stackexchange.com

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Suppose I need to evaluate the following sum: $$\sum_{k=2}^n \left[\frac{1}{k(k+2)}\right]$$ With partial fraction decomposition, I can get it into the following form: $$\sum_{k=2}^n ...

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