Infinite series sum can't find the geometric series: $\sum_{i=0}^\infty (2^i +4^i)/6^i $

Question

$$\sum_{i=0}^\infty \frac{2^i +4^i}{6^i} $$

I'm not able to get a geometric series out of this. If I can the geometric series, the infinite summation from there is easy

Answer 1

HINT: $$\sum_{i=0}^\infty \dfrac{2^i+4^i}{6^î} =\sum_{r=0}^\infty\left(\dfrac26\right)^r+\sum_{r=0}^\infty\left(\dfrac46\right)^r$$

as both the series converge as $0<\dfrac26<\dfrac46<1$

using for $|r|<1,$ $$\sum_{n=0}^\infty ar^n=\dfrac a{1-r}$$