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Why both Wolfram Alpha and Wolfram Cloud don't simplify below BBP type sum, which I came up with?

Alexander Povolotsky
Posted 2 years ago
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Sum.nb
POSTED BY: Alexander Povolotsky
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With Mathematica I get simplification with FullSimplify, but not with Simplify alone.
POSTED BY: Gianluca Gorni

And also https://www.dcode.fr/summation-calculator does not produce the desired final result

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Screenshot_20230...png
POSTED BY: Alexander Povolotsky

http://drhuang.com/science/mathematics/software/
doesn't produce the final result either
POSTED BY: Alexander Povolotsky

Thanks, Dear Gianluca!
POSTED BY: Alexander Povolotsky
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