Assistance on a recursive proof

[black_hole]

Homework Statement

Define a sequence of numbers A_i by: A₀ = 2, A_n+1 = A_n/2 + 1/A_n (for n greater than or equal to 1). Prove that A_n less than or equal to √(2) + 1/2ⁿ for all n greater than or equal to 0. I think it's a safe bet that induction should be used here. I'm having trouble finding the inductive step though maybe just cause I'm not feeling particularly well today. Help is always appreciated.

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

hi black_hole!

I think it's a safe bet that induction should be used here.

yes …

just put it into the equation! ​