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If the series Sigma an convergent absolutely,then which of the following is true? A. There exists a rearrangement of sigma an which diverges to infinity . B. There exists a rearrangement of sigma an which diverges to -infinity. C. There exists a rearrangement of sigma an which converges with different sum than sigma an. D. Every rearrangement of sigma an converges with the same sum as sigma an.?
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If the series Sigma an convergent absolutely,then which of the followi...
Answer:
A. There exists a rearrangement of sigma an which diverges to infinity.
- If a series Σan converges absolutely, then it means that the rearrangement of the terms will not affect the convergence of the series.
- However, it is possible to rearrange the terms in such a way that the series diverges to infinity.
- This implies that there exists a rearrangement of Σan which diverges to infinity.
Explanation:
- Absolute convergence ensures that rearranging the terms of the series will not change the convergence behavior of the series.
- However, rearranging the terms can lead to different sums for the series.
- In the case of absolute convergence, the rearranged series will still converge to the same sum as the original series.
- Therefore, option A is true in this scenario.
A. There exists a rearrangement of sigma an which diverges to infinity.
- If a series Σan converges absolutely, then it means that the rearrangement of the terms will not affect the convergence of the series.
- However, it is possible to rearrange the terms in such a way that the series diverges to infinity.
- This implies that there exists a rearrangement of Σan which diverges to infinity.
Explanation:
- Absolute convergence ensures that rearranging the terms of the series will not change the convergence behavior of the series.
- However, rearranging the terms can lead to different sums for the series.
- In the case of absolute convergence, the rearranged series will still converge to the same sum as the original series.
- Therefore, option A is true in this scenario.
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If the series Sigma an convergent absolutely,then which of the following is true? A. There exists a rearrangement of sigma an which diverges to infinity . B. There exists a rearrangement of sigma an which diverges to -infinity. C. There exists a rearrangement of sigma an which converges with different sum than sigma an. D. Every rearrangement of sigma an converges with the same sum as sigma an.?
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If the series Sigma an convergent absolutely,then which of the following is true? A. There exists a rearrangement of sigma an which diverges to infinity . B. There exists a rearrangement of sigma an which diverges to -infinity. C. There exists a rearrangement of sigma an which converges with different sum than sigma an. D. Every rearrangement of sigma an converges with the same sum as sigma an.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the series Sigma an convergent absolutely,then which of the following is true? A. There exists a rearrangement of sigma an which diverges to infinity . B. There exists a rearrangement of sigma an which diverges to -infinity. C. There exists a rearrangement of sigma an which converges with different sum than sigma an. D. Every rearrangement of sigma an converges with the same sum as sigma an.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the series Sigma an convergent absolutely,then which of the following is true? A. There exists a rearrangement of sigma an which diverges to infinity . B. There exists a rearrangement of sigma an which diverges to -infinity. C. There exists a rearrangement of sigma an which converges with different sum than sigma an. D. Every rearrangement of sigma an converges with the same sum as sigma an.?.
If the series Sigma an convergent absolutely,then which of the following is true? A. There exists a rearrangement of sigma an which diverges to infinity . B. There exists a rearrangement of sigma an which diverges to -infinity. C. There exists a rearrangement of sigma an which converges with different sum than sigma an. D. Every rearrangement of sigma an converges with the same sum as sigma an.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the series Sigma an convergent absolutely,then which of the following is true? A. There exists a rearrangement of sigma an which diverges to infinity . B. There exists a rearrangement of sigma an which diverges to -infinity. C. There exists a rearrangement of sigma an which converges with different sum than sigma an. D. Every rearrangement of sigma an converges with the same sum as sigma an.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the series Sigma an convergent absolutely,then which of the following is true? A. There exists a rearrangement of sigma an which diverges to infinity . B. There exists a rearrangement of sigma an which diverges to -infinity. C. There exists a rearrangement of sigma an which converges with different sum than sigma an. D. Every rearrangement of sigma an converges with the same sum as sigma an.?.
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