Alternative way to prove that the sum of the square reciprocals is ${\pi^2}/6$

Asked Jul 31 '16 at 17:33

Active Jul 31 '16 at 18:57

Viewed 41 times

When I learned about how the sum of a series could be divergent and convergent, I decided to try to find the sum of the square reciprocals to no avail. The proof, obviously at not my level as you can tell, was too difficult to understand (what math branch is required because they mentioned something a Riemann Zeta function).

Is there an alternative proof that would yield the result ${\pi^2}/6$ as well without higher math?

edited Jul 31 '16 at 18:57

z100

asked Jul 31 '16 at 17:33

Ian L

Well can you at least answer my question to what branch of math this is? – Ian L Jul 31 '16 at 17:43
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Have a look at the linked post, which contains many proofs... involving many branches of math. – Clement C. Jul 31 '16 at 17:45
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You can use Fourier analysis. – velut luna Jul 31 '16 at 17:45
The sum is $\pi^2/6$, not $\pi/6$ – Peter Jul 31 '16 at 18:20
Thank you. I have fixed that. – Ian L Jul 31 '16 at 18:31

Alternative way to prove that the sum of the square reciprocals is ${\pi^2}/6$

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