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Mock AIME 4 2006-2007 Problems/Problem 13

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Problem

The sum

$\sum_{k=1}^{2007} \arctan\left(\frac{1}{k^2+k+1}\right)$

can be written in the form $\arctan\left(\frac{m}{n}\right)$, where $\gcd(m,n) = 1$. Compute the remainder when $m+n$ is divided by 100.

Solution

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