Friday, 28 February 2014

real analysis - Show x1=2,xn+1=fracx2n+22xnsqrt2

I want to show that x1=2,xn+1=x2n+22xn is a convergent sequence and thus want to bound it below by 2. I tried to use induction but my problem is that if xn>2 then the denominator is greater than 4 but the denominator is less than 122 so they compete against each other. How can solve this issue?

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