Zeta[2]=(Pi^2)/6

Question:
Can you please tell me a proof that Zeta[2]=(Pi²)/6

Thanks

Hi Alex,

If you know what a Fourier series is, then a very easy proof would be accessible to you -- you can find it in any text that introduces Fourier series. It also follows from other advanced concepts, so it can be found in many books on analysis or complex analysis.

Elementary proofs appear frequently in math journals.

Examples:

In the AMERICAN MATHEMATICAL MONTHLY

68 (1961) 485-487
80:4 (1973) 424-425 and also 425-431
85:6 (1978) 481-483
94:7 (1987) 662-663

Also, there is a proof in MATHEMATICS MAGAZINE 45:3 (1972) 148-149.

Most of these articles list further examples in their references.

If you would like us to send you a copy of one of these articles, please let us know.

Chris Go to Math Central