Yeah, a Telescoping Sum..

Algebra Level 5

The value of

k=0997(1)kk3+9k2+26k+24(997k)\displaystyle \sum_{k=0}^{997} \frac{(-1)^k}{k^3+9k^2+26k+24}\binom{997}{k}

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

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