For c>0, consider the following quadratic equation:


=0 , x>0
Define the sequence {
} recursively fixing
> 0 and then, if n is an index for which {
} has been defined, defining
= sqrt{c+x_n}
Prove that the sequence {
} converges monotonically to the solution of the above equation!

I tried to attempt this problem by setting
= 1, and creating a sequence. It turns out to be a monotonic incereasing sequence. But how do we show that the sequence converges to the solution of the quadratic equation?
Also I am unclear about the starting value of
. Is it ok to start with
= 1, or does the starting value have to be another number?