Re: A Formula for Pi

On 20-06-2008 7:16, Maury Barbato wrote:

I found in the book "The Penguin Dictionary of
Curious and Interesting Numbers" by Wells the following formula involving pi

(pi - 3)/4 =

= sum_{k=1 to infty}[(-1)^(k+1)]/[2k*(2k+1)*(2k+2)]

Is there anybody who knows a proof of this wonderful
series?

You already got a reply. I only want to remark that the formula is
equivalent to

pi - 3 = sum_{k = 1 to oo}(-1)^{k + 1}/(k(2k + 1)(k + 1)

= sum_{k = 1 to oo}(-1)^{k + 1}/(1^2 + 2^2 + ... + k^2).

Best regards,

Jose Carlos Santos
.