Mathematics · Real Analysis
Let {an}n ≥ 1 be a bounded sequence of real numbers. According to the Bolzano-Weierstrass theorem, which of the following statements must be true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1There is at least one subsequence of {an}n ≥ 1 which is convergent✓
- 2All subsequences of {an}n ≥ 1 converge to the same limit
- 3There is exactly one subsequence of {an}n ≥ 1 which is convergent
- 4Every subsequence of {an}n ≥ 1 is convergent
Correct answer
There is at least one subsequence of {an}n ≥ 1 which is convergent
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