Big, ugly, but not so complicated

Algebra Level 4

n=220171nk=2n(1+1k)\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 ab\dfrac {a}{b}, where aa and bb are coprime positive integers. Find a+ba+b.

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