* In this question, you may not use the fact that Cauchy sequences are equivalent to...

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* In this question, you may not use the fact that Cauchy sequences are equivalent to conver- gent sequences. Let (an) nEN CR be a Cauchy sequence such that there exists a convergent subsequence to some limit a R. Show that the original sequence converges to a R. You should be able to prove this just from first principles. * In this question, you may not use the fact that Cauchy sequences are equivalent to conver- gent sequences. Let (an) nEN CR be a Cauchy sequence such that there exists a convergent subsequence to some limit a R. Show that the original sequence converges to a R. You should be able to prove this just from first principles.