Answer
$4$
Work Step by Step
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
Since, we have $\sum_{n =1}^{ \infty}\dfrac{2^n+3^n}{4^n}=\sum_{n =1}^{ \infty} (\dfrac{1}{2})^n+\sum_{n =0}^{ \infty} (\dfrac{3}{4})^n$
Both series are convergent geometric series with first term, $a=\dfrac{1}{2},\dfrac{3}{4}$ and common ratio $r =\dfrac{1}{2},\dfrac{3}{4}$
Thus, $S=\dfrac{1/2}{1-\dfrac{1}{2}}+\dfrac{3/4}{1-\dfrac{3}{4}}=1+3=4$
