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Algebra Level 4

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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