The next year summation

Algebra Level 5

n=12017n12+23++n(n+1) \large \displaystyle \sum_{n=1}^{2017} \dfrac{n}{1\cdot2+2\cdot3+\cdots +n(n+1)}

If the above expression is in the form AB \dfrac{A}{B}, where AA and BB are coprime positive integers, find A+BA+B.


This problem is original.

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