A Formula for Pi

Hello,
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?

Thank you very much for your attention.
My Best Regards,
Maury Barbato
.