Why do I love 2015 so much #2

Algebra Level 5

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

Find \(A+B\) where \(A,B\) are positive coprime integers.

This problem is a part of this set.