Write some code to prove that $\sum_{k=1}^n\tan^{-1}\frac{1}{2k^2}=\tan^{-1}\frac{n}{n+1}$. Note the right-hand side depends only on $n$, the numbers of terms in your sum on the left-hand side. (From Andreescu, p. 28.)← Back to challenges | Lessons

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