(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a_{n+1}=a_{n}/2 + 1/a_{n}

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 a_{0}. I found that the sequence is approaching square root of two when a_{0}is positive, and negative of square root of positive when a_{0}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 a_{n}approximate to a_{n+1}when n is approaching infinity? If so how can I prove it? Can I substitute both a_{n}and a_{n+1}with a_{infinity}and find the limit?

Thanks in advanced.

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# Homework Help: Limit of sequence

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