I am asked to determine whether or not the following series converges or diverges:
$\sum_{n=1}^\infty C_n$ where $C_1 = 2$ and $C_{n+1} = \sqrt{C_n+1}$
Now my first thought was to determine if {$C_n$} diverges else this will tell me that the series diverges. But based on my calculations the sequence seems to converge. So I can't conclude anything there. My next bet was to try to determine if the limit of C$_n$ is 0 as n tends to infinity. However, I got stuck there. I also tried using the ratio test but again, I got stuck. Can anyone give me a hint as to what might be a good approach?