Let a sequence {xn} from n=1 to infinity satisfy x_(n+2)=sqrt(x_(n+1) *xn) for n=1,2 ...... 1. Prove...

Let a sequence {xn} from n=1 to infinity satisfy

x_(n+2)=sqrt(x_(n+1) *xn) for n=1,2 ......

1. Prove that a<=xn<=b for all n>=1

2. Show |x_(n+1) - xn| <= sqrt(b)/(sqrt(a)+sqrt(b)) * |xn - x_(n-1)| for n=2,3,.....

3. Prove {xn} is a cauchy sequence and hence is convergent

Please show full working for 1,2 and 3.

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Expert Solution

Colby Messinger answered 9 months ago

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