What is \frac{3}{1^{2}\times2^{2}}+\frac{5}{2^{2}\times3^{2}}+\frac{7}{3^{2}\times4^{2}}+... equal to ?

Explanation

The general term is \frac{2n+1}{n^2(n+1)^2}, which can be split using partial fractions as \frac{1}{n^2} - \frac{1}{(n+1)^2}. This forms a telescoping series: (1 - 1/4) + (1/4 - 1/9) + \dots = 1.

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