## Thomas' Calculus 13th Edition

Let us consider $a_n=\lim\limits_{n \to \infty} \dfrac{2^n}{n+1}$ Here, $\lim\limits_{n \to \infty} \dfrac{2^n}{n+1}=\dfrac{\infty}{\infty}$ This shows that the limit has an indeterminate form so, we will use L-Hospital's rule. so, $\lim\limits_{n \to \infty} \dfrac{(2^n) (\ln 2)}{1} =\infty$ Thus, the series is divergent.