A short elementary proof of 1/k2=2/6

نویسنده

  • Daniel Daners
چکیده

We give a short elementary proof of the well known identity ζ(2) = ∑∞ k=1 1/k 2 = π/6. The idea is to write the partial sums of the series as a telescoping sum and to estimate the error term. The proof is based on recursion relations between integrals obtained by integration by parts, and simple estimates. Introduction The aim of this note is to give a truly elementary proof of the identity

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تاریخ انتشار 2012