Answer
Diverges
Work Step by Step
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
Since, we have $\sum_{n =1}^{ \infty}\dfrac{2^n+4^n}{3^n+4^n}=\sum_{n =1}^{ \infty}\dfrac{(\dfrac{1}{2})^n+1}{(\dfrac{3}{4})^n+1}=\dfrac{1}{1}= 1\ne 0$
Thus, the given series $\sum_{n =1}^{ \infty}\dfrac{2^n+4^n}{3^n+4^n}$ diverges as per the nth term integral test.