Evaluate $\sum_{i=1}^{\infty}\prod_{j=1}^{i}\frac{j-\frac{1}{2}}{j\left(j+\frac{1}{2}\right)^2}$

by Power ranger   Last Updated July 12, 2019 10:20 AM - source

We want to evaluate this formula sum,

$$\sum_{i=1}^{\infty}\prod_{j=1}^{i}\frac{j-\frac{1}{2}}{j\left(j+\frac{1}{2}\right)^2}$$



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