Wednesday, 27 March 2019

calculus - Prove that sumfrac1n2=fracpi26

In this answer two sequences are mentioned.
In particular, I would like to prove that



+n=11n2=π26



If I knew that the sequence converges to π26, I could use the ϵ-M criterion to prove the convergence to that value.



But how to prove that the above sequence converges to that value if I don't know the value itself? Is there a general way to proceed in such cases?

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