Answer
Diverges
Work Step by Step
Consider $a_n=\lim\limits_{n \to \infty} \dfrac{2^n}{n+1}$
But $\lim\limits_{n \to \infty} \dfrac{2^n}{n+1}=\dfrac{\infty}{\infty}$
Need to apply L-Hospital's rule.
$\lim\limits_{n \to \infty} \dfrac{2^n \ln 2}{1} =\infty $
Hence, the given series diverges.
