Question:
Let (an) and (bn) be sequences of real numbers such that
\(|a_n-a_{n+1}|=\frac{1}{2^n}\) and \(|b_n-b_{n+1}|=\frac{1}{\sqrt{n}}\) for n ∈ \(\N\).
Then
Let (an) and (bn) be sequences of real numbers such that
\(|a_n-a_{n+1}|=\frac{1}{2^n}\) and \(|b_n-b_{n+1}|=\frac{1}{\sqrt{n}}\) for n ∈ \(\N\).
Then
\(|a_n-a_{n+1}|=\frac{1}{2^n}\) and \(|b_n-b_{n+1}|=\frac{1}{\sqrt{n}}\) for n ∈ \(\N\).
Then
Updated On: Oct 1, 2024
- both (an) and (bn) are Cauchy sequences
- (an) is a Cauchy sequence but (bn) need NOT be a Cauchy sequence
- (an) need NOT be a Cauchy sequence but (bn) is a Cauchy sequence
- both (an) and (bn) need NOT be Cauchy sequences
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The Correct Option is B
Solution and Explanation
The correct option is (B) : (an) is a Cauchy sequence but (bn) need NOT be a Cauchy sequence.
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