# That's too much Gamma

Algebra Level 4

$\large \sum_{n=1}^{1729} \dfrac{\Gamma(n) \times \Gamma(n+1)}{\Gamma(n+1) \times \Gamma(n+2) }$

If the summation above is the form of $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

Notation: $$\Gamma(\cdot)$$ denotes the Gamma function.

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