Explicit sum of $\sum_{n=0}^{\infty} \frac{6+3^n}{6^{n+2}}$ I want to find the sum of the infinite series $$\sum_{n=0}^{\infty} \frac{6+3^n}{6^{n+2}}$$
So far I have managed to simplify the expression to $$\sum_{n=0}^{\infty} \left(\frac {1}{6^{n+1}} + \frac{1}{9\cdot2^{n+2}}\right)$$.
The sum clearly converges as both expressions are equal to $0$ as $\lim_{n\to\infty}$. Any tips as to how I may find an explicit expression for the sum of this series?
thanks in advance

for the finite sum we have $$\sum_{n=0}^k\frac{6+3^n}{6^{n+2}}=-4/5\,{\frac {6+{3}^{k+1}}{{6}^{k+3}}}-{\frac {72+12\,{3}^{k+2}}{5\,{6
}^{k+4}}}+{\frac{23}{90}}
$$ now compute the limit for $k$ tends to infinity
