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Published in:
2004 | OriginalPaper | Chapter
Three times π2/6
Authors : Martin Aigner, Günter M. Ziegler
Published in: Proofs from THE BOOK
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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We know that the infinite series $$ \sum\nolimits_{n \ge 1} {\frac{1}{n}} $$ does not converge. Indeed, in Chapter 1 we have seen that even the series $$ \sum\nolimits_{p \in p} {\frac{1}{p}} $$ diverges. However, the sum of the reciprocals of the squares converges (although very slowly, as we will also see), and it produces an interesting value.