An elementary proof of $\,\sum_{n \ge 1}{1/n^2} = π^2/6\,$ and a recurrence formula for even zeta values

Details An elementary proof of $\,\sum_{n \ge 1}{1/n^2} = π^2/6\,$ and a recurrence formula for even zeta values An elementary proof of $\,\sum_{n \ge 1}{1/n^2} = π^2/6\,$ and a recurrence formula for even zeta values

2011-09-19

arxiv.org/abs/1109.4605v3

Mathematics

History and Overview

5 pages, no figures. Small corrections, some examples added at the end of the paper. Submitted to Coll. Math. Journal (03/26/2

Scientific paper

In this note, a series expansion technique introduced recently by Dancs and He for generating Euler-type formulae for $\:\zeta{(2k+1)}$, $\,k\,$ being a positive integer and $\zeta{(s)}$ being the Riemann zeta function, is modified in a manner to furnish the even zeta values $\,\zeta{(2k)}$. As a result, I find an elementary proof of $\:\sum_{n=1}^\infty{{1/{n^2}}} = {\,\pi^2/6}\,$ and a recurrence formula for $\zeta{(2k)}$.

Affiliated with

Also associated with

No associations

Rating

An elementary proof of $\,\sum_{n \ge 1}{1/n^2} = π^2/6\,$ and a recurrence formula for even zeta values does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An elementary proof of $\,\sum_{n \ge 1}{1/n^2} = π^2/6\,$ and a recurrence formula for even zeta values, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An elementary proof of $\,\sum_{n \ge 1}{1/n^2} = π^2/6\,$ and a recurrence formula for even zeta values will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-97715