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# Quick Question

+1
336
3
+4322

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

Nov 29, 2018

### 3+0 Answers

#1
+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
+700
0

Probably from some online math website.

Nov 29, 2018
#3
+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