# Lawrence's sum

Algebra Level 4

If the sum

$\sum_{n=1}^{2111} \frac{n+2}{n! + (n+1)! + (n+2)!}$

is written as $$\frac{1}{2} - \frac{1}{a!}$$, what are the last three digits of $$a$$?

This problem is posed by Lawrence L.

Details and assumptions

The last three digits of $$1023$$ is $$023$$. You may enter your answer as $$023$$ or $$23$$.

×