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Compute
\(\sum_{m = 1}^\infty \sum_{n = 1}^\infty \frac{m^2 n}{3^m (n3^m + m3^n)}.\)

 Nov 29, 2018
 #1
avatar+5797 
+1

Mathematica couldn't come up with an answer so I'm not going to try either.

 

Where did you get this problem?

 Nov 29, 2018
 #2
avatar+700 
0

Probably from some online math website.

 Nov 29, 2018
 #3
avatar+28135 
+2

Numerically, this seems to converge (very quickly) to 9/32.  This is such a simple result I suspect there is a way of finding it analytically. However, I have so far failed to do so!!

 Nov 29, 2018

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