Conditional vs absolute

$\sqrt{n+1}-\sqrt{n}=1/(\sqrt{n+1}+\sqrt{n})$ decreases to 0, so the alternating series converges (Leibniz). The absolute series behaves like $\sum 1/(2\sqrt{n})$, which diverges. Hence conditionally convergent — option 3 is the most precise true statement (official key: 3).