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Let a₁, a₂,..., anₙ, be a sequence of rational numbers. The sequence is called a Cauchy sequence if for every positive real number ε, there is a natural number N, such that for all m, n € N, m,n ≥ N ⇒ ∣aₘ−aₙ​∣ < ε.Prove that the sequence 1,1/2,1/4,1/8,....,1/2ₙ,...... is a Cauchy sequence.

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