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Algebra Level 4

Let aa be a real number such that

a=11+13+16+110++15050.a=\frac{1}{1}+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\cdots+\frac{1}{5050}.

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

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