# Yeah, a Telescoping Sum..

Algebra Level 5

The value of

$\displaystyle \sum_{k=0}^{997} \frac{(-1)^k}{k^3+9k^2+26k+24}\binom{997}{k}$

Can be expressed in the form $$\frac{m}{n}$$. Where $$m$$ and $$n$$ are coprime positive integers, find $$m+n$$.

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