Bounded and Unbounded Sequence MCQ Quiz - Objective Question with Answer for Bounded and Unbounded Sequence - Download Free PDF
Last updated on Mar 10, 2025
Latest Bounded and Unbounded Sequence MCQ Objective Questions
Bounded and Unbounded Sequence Question 1:
Every bounded sequence of real numbers has a convergent subsequence.
Answer (Detailed Solution Below)
Bounded and Unbounded Sequence Question 1 Detailed Solution
Solution-
Bolzano - Weierstrass Theorem- The theorem states that each infinite bounded sequence in has a convergent subsequence.
An equivalent formulation is that a subset of is sequentially compact if and only if it is closed and bounded.
Therefore, Correct Option is Option 3).
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Bounded and Unbounded Sequence Question 2:
Every bounded sequence of real numbers has a convergent subsequence.
Answer (Detailed Solution Below)
Bounded and Unbounded Sequence Question 2 Detailed Solution
Solution-
Bolzano - Weierstrass Theorem- The theorem states that each infinite bounded sequence in has a convergent subsequence.
An equivalent formulation is that a subset of is sequentially compact if and only if it is closed and bounded.
Therefore, Correct Option is Option 3).