Answer
$4$
Work Step by Step
Formula to calculate the sum of a geometric series is:
$S=\dfrac{a}{1-r}$;
Since, we have two series $\sum_{n =1}^{ \infty}\dfrac{2^n+3^n}{4^n}=\sum_{n =1}^{ \infty} (\dfrac{1}{2})^n+\sum_{n =0}^{ \infty} (\dfrac{3}{4})^n$
Here, $a=\dfrac{1}{2},\dfrac{3}{4}$ and common ratios are: $r =\dfrac{1}{2},\dfrac{3}{4}$
Now, Thus, $S=s_1+s_2=\dfrac{1/2}{1-\dfrac{1}{2}}+\dfrac{3/4}{1-\dfrac{3}{4}}$
or, $=1+3$
or, $=4$
