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Sum $\sum^\infty_{n=1}\frac{(-1)^nH_n}{(2n+1)^2}$
I would like to seek your assistance in computing the sum
$$\sum^\infty_{n=1}\frac{(-1)^nH_n}{(2n+1)^2}$$
I am stumped by this sum. I have tried summing the residues of $\displaystyle f(z)=\frac{\pi\...
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