Re: Zeta(1)

From: Oscar Lanzi III (ol3_at_webtv.net)
Date: 03/02/05 

Date: Tue, 1 Mar 2005 18:38:24 -0600

But back to the original question. Define f(x) = x for 0 <=x <= pi.
Obtain the Fourier cosine series for this (set f(-x) = f(x) and then
consider f to have a period of 2*pi). Set the series to f(0) = 0 at x =
0 and you should find that the sum of the odd-numbered terms in zeta(2)
is pi^2/8. Multiply by the geometric series 1 + 1/2^2 + 1/4^2 + 1/8^2
+... = 4/3 to pull in the even-numbered terms.

--OL