Limit of a recursive succession

[wild-night]

Homework Statement

Find the limit of the following succession:

a₁ = sqrt(b)

a_n+1 = sqrt(b + a_n)

where b>0 is a real number.


I've thought about this really hard and could´t come up with an answear.
Please help!

 

[╔(σ_σ)╝]

lim a_(n+1) = lim sqrt(b+a_n) , right?

Do you agree that
lim a_n+1 = lim a_n =x ? (I assume we have already shown the sequence has a limit)

If so then,

x = sqrt(b+ x)

x^2 -x-b=0

Your limit is one of the solutions to that polynomial.