Difference between revisions of "G285 2021 Fall Problem Set Problem 8"
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==Problem== | ==Problem== | ||
| − | If the value of <cmath>\sum_{a=1}^{\infty} \sum_{b=1}^{\infty} \sum_{c=1}^{\infty} \frac{a+2b+3c}{4^(a+b+c)}</cmath> can be represented as <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime. Find <math>m+n</math>. | + | If the value of <cmath>\sum_{a=1}^{\infty} \sum_{b=1}^{\infty} \sum_{c=1}^{\infty} \frac{a+2b+3c}{4^{(a+b+c)}}</cmath> can be represented as <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime. Find <math>m+n</math>. |
==Solution== | ==Solution== | ||
Geometric series spam | Geometric series spam | ||
Revision as of 11:39, 11 July 2021
Problem
If the value of ![\[\sum_{a=1}^{\infty} \sum_{b=1}^{\infty} \sum_{c=1}^{\infty} \frac{a+2b+3c}{4^{(a+b+c)}}\]](http://latex.artofproblemsolving.com/8/3/e/83e4f5da4b3b44825dcf84447f1deb0711d88c15.png)
can be represented as 
, where 
and 
are relatively prime. Find 
.
Solution
Geometric series spam
