G285 2021 Fall Problem Set Problem 8

Problem

If the value of $\sum_{a=1}^{\infty} \sum_{b=1}^{\infty} \sum_{c=1}^{\infty} \frac{a+2b+3c}{4^{(a+b+c)}}$ can be represented as $\frac{m}{n}$ , where $m$ and $n$ are relatively prime. Find $m+n$ .

Solution

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G285 2021 Fall Problem Set Problem 8

Problem

Solution