An algebra problem by Christian Daang

Algebra Level 5

n=41(n2)(n1)n(n+1)(n+2)\large \sum_{n = 4}^\infty \dfrac{1}{(n-2)(n-1)n(n+1)(n+2)}

The infinite sum above can be expressed as ab\dfrac{a}{b} , where aa and bb are coprime positive integers, find a+ba + b.

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