An algebra problem by Darel Gunawan

Algebra Level 3

Given that : 1232+1333+1434++11003100=ab\frac{1}{2^3-2} +\frac{1}{3^3-3}+\frac{1}{4^3-4}+ \cdots +\frac{1}{100^3-100} = \frac{a}{b}

where aa and bb are coprime positive integers. What is the value of a+ba+b ?

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