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Let (an)∞n=1 be a monotone sequence. Let (ank )∞k=1 be a subsequence of (an). Prove that...

Let (an)∞n=1 be a monotone sequence. Let (ank )∞k=1 be a subsequence of (an). Prove that (an) converges iff (ank) converges. Also, prove that if the two sequences converge, their limits are the same.

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