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Let $a$ be a real number such that

$a=\frac{1}{1}+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\cdots+\frac{1}{5050}.$

If $a$ can be expressed in the form $\frac{x}{y}$, where $x,y$ are coprime, positive integers, find $x+y$.

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