I would like to get a hint on how to establish the convergence of the following sequence:
$a_{n+1}= a_n + \frac{\sqrt{\vert a_n \vert }}{n^2}$
where $a_1$ is arbitrary. This is an increasing sequence, so if I could show that it was bounded above I would be done. I cannot figure out how to do that. Any help would be appreciated.