Mathematics · Real Analysis
Let {x n } be a sequence of positive real numbers. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If the sequence {x n } is unbounded, then every subsequence is unbounded.
- 2If lim n → ∞ (x n+1 / x n ) exists, then {(x n ) 1/n } is bounded.✓
- 3If {(-1) n x n } converges, then the sequence {x n } converges.
- 4If the two subsequences {x 2n } and {x 2n+1 } converge, then the sequence {x n } converges.
Correct answer
If lim n → ∞ (x n+1 / x n ) exists, then {(x n ) 1/n } is bounded.
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