how do i use this formula to evaluate the sum of the even terms
(equation inside)

Question

anonymous · Answer

$$sum_{n=1}^{infty} 1/(2n)2$$

anonymous · Answer

well I have no idea what that is.
It didn't work

amistre64 · Answer

$$\sum_{n=1}^{\infty}\ \frac{1}{(2n)^2}$$

anonymous · Answer

$$\sum_{n=1}^{\infty}\frac{1}{(2n)^2}$$

anonymous · Answer

The script must be failing i can't read if i've laid that out correct

amistre64 · Answer

write out a sequence and see if you can construct a new summer from it

anonymous · Answer

Now it's working.. satellite73 that is the question.. how do i go about solving it?

anonymous · Answer

$$1/4+1/16+1/36+1/64+1/100$$

jamesj · Answer

Actually, the way you deal with this in contemporary mathematics is with an integral in the complex plane.  Easyish to explain with a blackboard where I can draw diagrams easily, annoying to do it here.

For the record, the answer is pi^2/24.

anonymous · Answer

hrmm... Thanks james.. I really need to find a way to show working.

amistre64 · Answer

$$\sum_{j=1}^{\infty}2k\ \sum_{n=k}^{\infty}\ \frac{1}{(2n)^2}$$ hmmmmm

jamesj · Answer

For a classical proof, have a look at this ,around page 7 onwards

jamesj · Answer

http://www.maa.org/pubs/Calc_articles/ma045.pdf

jamesj · Answer

the result sum n = 1 to infty of 1/n^2 is called Euler's formula.  That's what is shown in the note I just linked to.  It gives pi^2/6

It should be straight-forward to imitate that derivation for your summand 1/(2n)^2

jamesj · Answer

Actually, it's even easier.  Just pull the 1/2^2 = 1/4 outside.

So what you just need to do is prove Euler's formula using what arrows you currently have in your analytical quiver.

jamesj · Answer

anyone there?  Anyway ... time for brunch!