Mathematics · Real Analysis
Let (an)n≥1 be a bounded sequence in ℝ. Which of the following statements is FALSE?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If sup{an | n ≥ 1} = inf{an | n ≥ 1}, then (an) is constant
- 2If sup{an | n ≥ 1} = lim infn→∞ an, then (an) is constant✓
- 3If inf{an | n ≥ 1} = lim supn→∞ an, then (an) is convergent
- 4If lim infn→∞ an = lim supn→∞ an, then (an) is convergent
Correct answer
If sup{an | n ≥ 1} = lim infn→∞ an, then (an) is constant
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