An algebra problem by Christian Daang

Algebra Level 5

\[\large \sum_{n = 4}^\infty \dfrac{1}{(n-2)(n-1)n(n+1)(n+2)}\]

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

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