Answer
Converges
Work Step by Step
Consider $a_n=\dfrac{2^n}{3+4^n}$ and $b_n=\dfrac{ 1}{2^n}$
Now, $\lim\limits_{n \to \infty}\dfrac{a_n}{b_n} =\lim\limits_{n \to \infty}\dfrac{\dfrac{2^n}{3+4^n}}{\dfrac{ 1}{2^n}}$
Thus, we have $ =\lim\limits_{n \to \infty} \dfrac{4^n}{3+4^n}$
or, $=1$
Hence, the series is a convergent series due to the limit comparison test.
