Let $\displaystyle a,c>0$, a sequence {$\displaystyle a_n$} is defined:

$\displaystyle a_1=c$

$\displaystyle a_{n+1}=\sqrt{a+a_n}$

(1) For which values of c the sequence gets lower, higher or does not change?

(2) Is there a limit in each case? Find it.

Okay, in the first case it's easy, because then $\displaystyle a_n=c$ for every n, and of course the limit is c.

Only I found some weird expressions for c depending on a:

I found that $\displaystyle a_{n+1}>a_n$ when: $\displaystyle c^2-c<a$, which I don't know how to turn it into a 'nicer' expression of c.

That's before trying to find the limit of them...

Thank you very much!