If you are not going to bother learning LaTeX, at least try to use the _ symbol to denote subscripts:

If you wanted to type it into LaTeX, here is the code: [tex]a_1=1[/tex] and [tex]a_n = (2+a_{n-1})^{1/2}[/tex]

Anyway, let . Then for all . So, is increasing showing that . If the limit exists, then it must satisfy . So, implies , so or . Since is increasing and , so you know , so it must be .