Assume (xn : n an element of the N) is cauchy sequence in the metric space (X,d) which has convergent subsequence. Prove (xn: n an element of N) is convergent. I used N to denote the set of natural numbers. Hint: Convergence implies cauchy but cauchy does not imply convergence. Also, if it is cauchy and has a convergent subsequence then it converges.