Why do I love 2015 so much #2

Algebra Level 5

∑n=12015n(n+2)(n+3)(n+4)=AB\large{\displaystyle \sum^{2015}_{n=1}\frac{n}{(n+2)(n+3)(n+4)}=\frac{A}{B}}

Find A+BA+B where A,BA,B are positive coprime integers.

This problem is a part of this set.
Akshat Sharda by Akshat Sharda
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