Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I found this sum in an old math problems book and it asks me to find its closed form. And for the life of me I can't find. Here it is


Any hits or suggestions are welcomed.

share|cite|improve this question
the first fraction of it make me think of $4cosh(2\pi)$ however I'm not sure how to put the rest with it. What's $|B_{2p}|$? Perhaps writing the partial fraction as on fraction as three different sums might help and try to find three different closed forms of sum? – user88595 Nov 10 '13 at 14:53
$|B_{2p}|$ is the absolute value for the Bernoulli numbers. I've tried splitting it into 3 sums and fiddling around with the bernoulli numbers, but no result. – Leonida Nov 10 '13 at 14:57
The term before the parenthesis is $8\zeta(2p)$, maybe that could lead to something useful? – Daniel Fischer Nov 10 '13 at 15:00
@DanielFischer Good point, I totally missed that. Maybe it helps! – Leonida Nov 10 '13 at 15:05
Seems to be slowly converging to $\approx -0.4$. The 1281-st partial sum is -0.39665. – David H Nov 10 '13 at 15:43

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.