- #1
Screwdriver
- 129
- 0
Homework Statement
Check out matt grime's post in this thread (it's the last one):
https://www.physicsforums.com/showthread.php?p=470773#post470773"
How exactly did he know that the sum could be represented as that double integral? Also, is there a method of converting sums like that to integrals (double or otherwise) for summands other than [itex]n^{-2}[/itex] such as [itex]n^{-7}[/itex] or something?
Homework Equations
[tex]\int_{0}^{1}\int_{0}^{1}\frac{1}{1-xy}dxdy=\sum_{n=1}^{\infty }\frac{1}{n^2}[/tex]
The Attempt at a Solution
Come to think of it, I don't even really see how that helps you, because the series expansion for the [itex]y[/itex] integral (after computing the [itex]x[/itex] integral) is the derivative of the series you're trying to find, so integrating it just brings you back to where you started. The only thing I was able to note was that:
[tex]\sum_{n=0}^{\infty} (xy)^n=\frac{1}{1-xy}[/tex]
Last edited by a moderator: