Solving a crazy infinite sum

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A nice infinite series
Math | Calculus | infinite sum
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Ankush's one from the pile of beautiful problem. Very beautiful use symmetry.

toyeshprakash
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So basically all problems like this can be reduced to various values of the digamma function.

zh
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Very nice solving sir 🙏😊, by the way i am the creator of this problem, this problem is already posted and solved in RMM.

ankushparcha