HMMT 2002 A8

Determine the value of the sum

$\frac{3}{1^{2} \cdot 2^{2}}+\frac{5}{2^{2} \cdot 3^{2}}+\frac{7}{3^{2} \cdot 4^{2}}+\cdots+\frac{29}{14^{2} \cdot 15^{2}} .$

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{224}{225}

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