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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