Convergence and Limit of a Converging Sequence

[Keesjan]

Homework Statement

a1=0 an+1=Sqrt(1+2an) n=1,2,3...

show that an converges and find the limit

Homework Equations

The Attempt at a Solution

I have seen something like this before but i can't remember how to solve this.

well i think i get that it becomes sqrt(1+2sqrt(1+2sqrt(1+2sqrt) ect
just don't know how to write it out so i can find the limit

 

[Fightfish]

Well, to find the limit it is not that difficult actually. Both a(n+1) and a(n) approach the same limit as n tends to infinity, so its just a matter of solving a quadratic equation really.

Takes a bit more effort to prove that it converges though *scratches head*