$\displaystyle{\sum _{ n=1 }^{ 2015 }{ \frac { { n }^{ 2 }+n+1 }{ \left( { n }^{ 2 }+n \right) \left( n+1 \right) ! } }}$ can be represented in the form $\dfrac { a }{ b }$, where $a$ and $b$ are coprime positive integers. Find the value of $a-b$.

Your answer seems reasonable.
Find out if you're right!