\[ \large \displaystyle \sum_{n=1}^{2017} \dfrac{n}{1\cdot2+2\cdot3+\cdots +n(n+1)} \]

If the above expression is in the form \( \dfrac{A}{B}\), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).

This problem is original.

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