Let (n) be a sequence in M and let a M and k 0....

  

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Let (n) be a sequence in M and let a € M and k ≥ 0. Suppose that d(a, xn+1) ≤ |k|d(a,xn) for all n E N. Let qn = g(n) be a number such that d(a, xn+1) ≤ an d(a, x₁) for all n E N. Give qn and the range R of values of k for which the sequence (rn) is convergent. Let (n) be a sequence in M and let a € M and k ≥ 0. Suppose that d(a, xn+1) ≤ |k|d(a,xn) for all n E N. Let qn = g(n) be a number such that d(a, xn+1) ≤ an d(a, x₁) for all n E N. Give qn and the range R of values of k for which the sequence (rn) is convergent.

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Given the inequality da xn1 k da xn for all n N we want to find the value of qn an... View the full answer