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

Consider the sequence [tex]\left x_{n}\{\right\}[/tex] defined by the recursion relation,

[tex] x_{n+1} = \frac{1}{2} \left( x_{n} + \frac{2}{x_{n}} \right) [/tex]

where x_{0}> 0.

Use the fact that "if a sequence of real numbers is monotonically decreasing and

bounded from below, then it converges" to prove that the sequence converges.

Show that it converges to [tex]\sqrt{2}[/tex].

2. Relevant equations

3. The attempt at a solution

No idea!

Any help would be greatly appreciated.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Recursion relation convergence

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