# That's too much Gamma

**Algebra**Level 3

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

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.