Answer
Diverges
Work Step by Step
Formula to calculate the sum of a geometric series is:
$S=\dfrac{a}{1-r}$;
Since, we have two series$\sum_{n =1}^{ \infty}\dfrac{2^n+4^n}{3^n+4^n}=\dfrac{\sum_{n =1}^{ \infty}(\dfrac{1}{2})^n+1}{\sum_{n =1}^{ \infty}(\dfrac{3}{4})^n+1}= 1\ne 0$
Hence, $\sum_{n =1}^{ \infty}\dfrac{2^n+4^n}{3^n+4^n}$ diverges as per Nth Term Integral test.
