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# Question [any help would be appreciated]

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Compute

$\sum^{2020}_{n=1} [\frac{1}{n^2} - \frac{1}{(n+1)^2}]$

Jul 26, 2021
edited by Guest  Jul 26, 2021

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Never mind this equation seems exceedingly obvious unless there's some trick I'm missing.

\begin{align*} \sum^{2020}_{n=1} [\frac{1}{n^2} - \frac{1}{(n+1)^2}] = \frac{1}{1} - \frac{1}{4} + \frac{1}{4} - \frac{1}{9} + \frac{1}{9} ... -\frac{1}{2020^2} + \frac{1}{2020^2} - \frac{1}{2021^2} \end{align*}

Thus, terms cancel and..

\begin{align*} 1 - \frac{1}{2021^2} \end{align*}

Jul 26, 2021