Answer
conditionally convergent.
Work Step by Step
Let us consider $a_n=\dfrac{1}{1+\sqrt n}$
Here, $f(n)=\dfrac{1}{1+\sqrt n} \implies f'(n)=\dfrac{-1}{(2\sqrt {n)}(1+\sqrt n)} \lt 0$
The negative sign shows that, the sequence $u_n$ is decreasing.
Thus, $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty}\dfrac{1}{1+\sqrt n}=\lim\limits_{n \to \infty}\dfrac{1/\sqrt n}{1/\sqrt n+1}=0$
So, the series converges by the Alternating Series Test.
Here, the series $\Sigma_{n=1}^\infty \dfrac{1}{n^{1/2}}$ shows a $p$-series having $p=\dfrac{1}{2}$,thus the series diverges
Therefore, the series do not converge absolutely this implies that the series is conditionally convergent.