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Every convergent sequence is monotonic. True or False?
Most Upvoted Answer
Every convergent sequence is monotonic. True or False?
False
Explanation:
Every convergent sequence is not necessarily monotonic. A sequence is said to be convergent if it approaches a specific limit as the number of terms increases. However, the sequence could still oscillate or alternate between increasing and decreasing values without being strictly monotonic.
- For example, the sequence {1, -1, 1, -1, 1, -1, ...} converges to 1, but it is not monotonic.
- Another example is the sequence {1, 1/2, 2/3, 3/4, 4/5, ...} which converges to 1, but it is also not monotonic.
Therefore, it is not accurate to say that every convergent sequence is monotonic. Monotonic sequences are specifically characterized by either being always increasing or always decreasing, with no oscillations or alternations in the direction of the terms.
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Every convergent sequence is monotonic. True or False?
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Every convergent sequence is monotonic. True or False? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Every convergent sequence is monotonic. True or False? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Every convergent sequence is monotonic. True or False?.
Every convergent sequence is monotonic. True or False? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Every convergent sequence is monotonic. True or False? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Every convergent sequence is monotonic. True or False?.
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