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Different methods to compute $\sum_{n=1}^\infty \frac{1}{n^2}$.
I just got the "New and Revised" edition of "Mathematics: The New Golden Age", by Keith Devlin. On p. 64 it says the sum is $\pi^2/6$, but that's way off. $\pi^2/6 \approx 1.64493406685$ whereas the sum in question is $\approx 1.29128599706$. I'm expecting the sum to be something interesting, but I've forgotten how to do these things.
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$\begingroup$The answer is indeed pretty interesting!
$ \sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6} $
This can be proven using complex analysis or calculus, or probably in many hundreds of other ways. One example of how to prove this is given here:
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