Answer
Divergent
Work Step by Step
We have: $a_k=\dfrac{k+1}{\sqrt k+1}$
Now, $\lim\limits_{k \to \infty} a_k=\lim\limits_{k \to \infty} \dfrac{k+1}{\sqrt k+1}$
Use L-hospitals Rule : $\lim\limits_{k \to \infty} a_k=\lim\limits_{k \to \infty} \dfrac{1}{\dfrac{1}{2 \sqrt k}}\\=\infty \ne 0 $
We conclude that the given series is divergent by the divergence test.
