Question 43
Compute
$$
\sum_{a_{1}=0}^{\infty} \sum_{a_{2}=0}^{\infty} \cdots \sum_{a_{7}=0}^{\infty} \frac{a_{1}+a_{2}+\cdots+a_{7}}{3^{a_{1}+a_{2}+\cdots+a_{7}}}
$$
$$
\sum_{a_{1}=0}^{\infty} \sum_{a_{2}=0}^{\infty} \cdots \sum_{a_{7}=0}^{\infty} \frac{a_{1}+a_{2}+\cdots+a_{7}}{3^{a_{1}+a_{2}+\cdots+a_{7}}}
$$