$\displaystyle\sum_{n=1}^{\infty}\frac{1}{n(n+\frac{1}{2})}$ i am trying to solve an integral and this ended up being last part I need, Wolfram alpha gives $4-2\ln{4}$ but I don't know how they actually got that value. can anyone help or give a starting point? telescoping series didn't work
2026-05-15 01:50:15.1778809815
Sum of series $\sum_{n=1}^{\infty}\frac{1}{n(n+\frac{1}{2})}$
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Hint: $a_n = \dfrac{4}{2n} - \dfrac{4}{2n + 1}$.