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Different methods to compute $\sum_{n=1}^\infty \frac{1}{n^2}$.
$\sum \frac{1}{n^2}= \frac{\pi^2}{6}$
There are a few proofs for that fact but can anybody see why is it "really" true? Talking in geometric terms for example.
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2There are some relatively geometric proofs here: http://math.stackexchange.com/questions/8337/different-methods-to-compute-sum-n-1-infty-frac1n2 – Qiaochu Yuan May 20 '11 at 08:33
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I am voting to close. – May 20 '11 at 08:45
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When you want to know that it is "really" true you usally look at the analytic proof not the geometric interpretation. – Listing May 20 '11 at 10:21
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@Qiaouchu Yuan: Thank you. I didn't know this question was suggested already. – Tau May 20 '11 at 10:22
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@Qiaochu: Even though there are many proofs, there should be room for an intuitive explanation, a 'why' answer is more than just 'how'. Would a rewording of the question to that effect be a question not likely to be closed? Naively $\pi$ has something to do with circles, and the summation not at all, and that warrants a human explanation in addition to the algebraic directions for the path between them. – Mitch May 20 '11 at 14:27
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@Mitch: by the OP's own admission it sounds like the previous thread answered his question, more or less. The OP is free to edit or re-ask the question and describe what is not satisfactory about the proofs in the other thread. – Qiaochu Yuan May 20 '11 at 14:29