Correct Answer - Option 2 : A convergent subsequence
Concept:
According to the Bolzano-Weierstrass theorem:
Every sequence in a closed and bounded set S in sequence Rn has a convergent subsequence (which converges to a point in S).
Proof: Every sequence in a closed and bounded subset is bounded, so it has a convergent subsequence, which converges to a point in the set because the set is closed.
Conversely, every bounded sequence is in a closed and bounded set, so it has a convergent subsequence.
Another Bolzano-Weierstrass theorem is:
Every bounded infinite set of real numbers has at least one limit point or cluster point.
