Proof of Zeta (2) Function: Short & Concise

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Homework Help Overview

The discussion revolves around proving the value of the Riemann zeta function at 2, specifically that \(\zeta(2) = \frac{\pi^2}{6}\). Participants are exploring methods to achieve a concise proof of this result.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to find a short proof, mentioning an initial lengthy approach involving inequalities related to sine and tangent functions. Some participants question the mathematical background required for a concise proof, suggesting that advanced topics like Fourier series or complex analysis may be necessary.

Discussion Status

The conversation is ongoing, with participants expressing a desire for a brief proof while also acknowledging the complexity of the topic. There is no explicit consensus on the approach to take, and multiple interpretations of what constitutes a "short" proof are being explored.

Contextual Notes

Participants are discussing the constraints of the homework context, including the expectation for a concise proof and the potential need for advanced mathematical knowledge. There is also a reference to external resources, indicating a search for additional information.

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Homework Statement



Find the shortest way possible to prove:

Homework Equations



[tex]\zeta (2)=\frac{\pi^{2}}{6}[/tex]

The Attempt at a Solution



I trying doing sinx < x < tanx if u know what I mean but it took me 6 pages.
I want a prove that is short and concise.
Also, can you guys please show full working?
 
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Is this really homework?

May I know what your mathematical background is?? I ask this because the shortest possible proofs will require quite some mathematical knowledge such as Fourier series or complex analysis.
 
micromass said:
Is this really homework?

May I know what your mathematical background is?? I ask this because the shortest possible proofs will require quite some mathematical knowledge such as Fourier series or complex analysis.

Yes, I just want the shortest possible prove, a really concise prove.
Show me the prove, and leave the rest for me, I'll understand it.
 

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