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Prove cauchy sequence and thus convergence

  1. Dec 14, 2011 #1
    Let (Xn) be a sequence satisfying

    |Xn+1-Xn| ≤ λ^n r

    Where r>0 and λ lies between (0,1). Prove that (Xn) is a Cauchy sequence and so is convergent.
  2. jcsd
  3. Dec 14, 2011 #2


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    I have a hunch that you could use two facts:

    1) for every ε > 0 there exists some natural number N such that λ^N r < ε
    2) the triangle inequality
  4. Dec 14, 2011 #3
    I posted the solution of that with r=1 in a similar thread called cauchy sequence problem
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