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  3. . suppose that the sequence (xn) satisfies |xn –

. Suppose that the sequence (xn) satisfies |xn –?| ? c | xn-1- ?|2 for all n. Show...

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Question

Advance Math

. Suppose that the sequence (xn) satisfies

|xn –?| ? c |xn-1- ?|2 for all n.

  1. Show by induction that c | xn- ?| ? c |x0 - ?|2n , and give some condition

That is sufficient for the convergenceof (xn) to ?.

  1. Use part a) to estimate the number of iterations needed toreach accuracy

|xn –?| < 10-12 in case c = 10 and|x0 –? |= 0.09.

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