Big, ugly, but not so complicated

Algebra Level 4

\[\large \displaystyle \sum_{n=2}^{2017} \dfrac {\frac{1}{n}}{\displaystyle \prod_{k=2}^{n} \left( 1+\frac{1}{k} \right)} \]

The above expression can be expressed in the form \(\dfrac {a}{b}\), where \(a\) and \(b\) are coprime positive integers. Find \(a+b\).

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