# Why not integrate it !!

Calculus Level 4

$\lim_{n\to \infty} \large\sum_{k=1}^{n} \frac{k^{3}+6k^{2}+11k+5}{ (k+3 )!}$

Now let the above sum be expressed in the form $\frac{a}{b}$ , where $$a$$ and $$b$$ are integers which are co-prime. Then find $$a+b$$.

If you think the summation may not converge to a finite limit then type $$22$$ as your answer

This was a problem given in one of our tests.

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