# Sumproduct For Next Year

Calculus Level 4

$\large \displaystyle \sum_{i=1}^{\infty} \left ( {\displaystyle \prod_{n=1}^{2017} (i+n)} \right)^{-1}$

If the value of above expression is in the form $$\dfrac{1}{a \cdot b!}$$, where $$a$$ and $$b$$ are positive integers with $$a<b$$, find $$a+b$$.

Bonus: Generalise it.

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