# AIME Problem

Consider the sequence defined by $$a_k = \frac{1}{k^2+k}$$ for $$k \geq 1$$.

Given that $$a_m + a_{m+1} + a_{m+2} + \ldots + a_{n-1} = \frac{1}{31}$$, for positive integers $$m$$ and $$n$$ with $$m < n$$. Find $$m+n$$.

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