Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Which of the following statements is FALSE?a)...
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Which of the following statements is FALSE?
- a)The series
is convergent. - b)A Cauchy sequence of real numbers need not be bounded.
- c)A sequence of real numbers need not be bounded.
- d)A sequence of real numbers is convergent if and only if it is a Cauchy squence.
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Which of the following statements is FALSE?a)The seriesis convergent.b...
Option 1:
The series
Proof:
We know n2 > n(n-1)
Expanding we get
It follows that an is bounded from above and hence convergent.
The series
Proof:
We know n2 > n(n-1)
Expanding we get
It follows that an is bounded from above and hence convergent.
Option 2 and 4:
A sequence {an} of real numbers is called a Cauchy sequence if for each ∈ > 0 there is a number N ∈ N so that if m, n > N then |an − am| < ∈.
If a real sequence {an} converges, then for every ε > 0, there exists N ∈ N such that |an − am| < ε ∀ n,m ≥ N
Convergent sequences are Cauchy sequences.
A Cauchy sequence of real numbers is bounded.
A sequence is a convergent sequence if and only if it is a Cauchy sequence.
A sequence {an} of real numbers is called a Cauchy sequence if for each ∈ > 0 there is a number N ∈ N so that if m, n > N then |an − am| < ∈.
If a real sequence {an} converges, then for every ε > 0, there exists N ∈ N such that |an − am| < ε ∀ n,m ≥ N
Convergent sequences are Cauchy sequences.
A Cauchy sequence of real numbers is bounded.
A sequence is a convergent sequence if and only if it is a Cauchy sequence.
Option 3:
A sequence of real numbers need not be bounded, a sequence can be bounded or not bounded.
A sequence of real numbers need not be bounded, a sequence can be bounded or not bounded.
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Which of the following statements is FALSE?a)The seriesis convergent.b)A Cauchy sequence of real numbers need not be bounded.c)A sequence of real numbers need not be bounded.d)A sequence of real numbers is convergent if and only if it is a Cauchy squence.Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Which of the following statements is FALSE?a)The seriesis convergent.b)A Cauchy sequence of real numbers need not be bounded.c)A sequence of real numbers need not be bounded.d)A sequence of real numbers is convergent if and only if it is a Cauchy squence.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is FALSE?a)The seriesis convergent.b)A Cauchy sequence of real numbers need not be bounded.c)A sequence of real numbers need not be bounded.d)A sequence of real numbers is convergent if and only if it is a Cauchy squence.Correct answer is option 'B'. Can you explain this answer?.
Which of the following statements is FALSE?a)The seriesis convergent.b)A Cauchy sequence of real numbers need not be bounded.c)A sequence of real numbers need not be bounded.d)A sequence of real numbers is convergent if and only if it is a Cauchy squence.Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Which of the following statements is FALSE?a)The seriesis convergent.b)A Cauchy sequence of real numbers need not be bounded.c)A sequence of real numbers need not be bounded.d)A sequence of real numbers is convergent if and only if it is a Cauchy squence.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is FALSE?a)The seriesis convergent.b)A Cauchy sequence of real numbers need not be bounded.c)A sequence of real numbers need not be bounded.d)A sequence of real numbers is convergent if and only if it is a Cauchy squence.Correct answer is option 'B'. Can you explain this answer?.
Solutions for Which of the following statements is FALSE?a)The seriesis convergent.b)A Cauchy sequence of real numbers need not be bounded.c)A sequence of real numbers need not be bounded.d)A sequence of real numbers is convergent if and only if it is a Cauchy squence.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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