Let (n) be a sequence defined by 2₁ = 1 and for n ≥ 2, 1 2+²-1 In Prove that (n) is Cauchy using the definition of Cauchy Sequence and then find its limit. Hint: Show that for all n ≥ 2, one has |£n+1 = £n] < } ]£n − En-1. The triangle inequality and geometric se- ries formula may be useful after this.

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