2015

Calculus Level 3

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

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