This is hard 2

Calculus Level 4

\[ \sum_{n=1}^{2011} \left ( \dfrac{n^2+n+1}{(n^2 + n) (n + 1)!} \right )\]

If the above summation can be stated in the form of \( \frac {a!-b!-1}{a!-b!} \), find a + b.

Thanks to Math man - title taken from math man's problem - This is hard

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