1. The problem statement, all variables and given/known data an+1=an/2 + 1/an Prove that the above sequence converge and find the limit. 2. Relevant equations 3. The attempt at a solution I have used Maple 12 to compute up to 10 term, using different initial value of a0. I found that the sequence is approaching square root of two when a0 is positive, and negative of square root of positive when a0 is negative. From the software, I know that the sequence is convergent, but it is rather difficult to find a mathematical proof. Is it reasonable to say that an approximate to an+1 when n is approaching infinity? If so how can I prove it? Can I substitute both an and an+1 with ainfinity and find the limit? Thanks in advanced.