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The series Sigma n=1 dask to infinity (-1)^n/2n+1 is A. not alternating B. alternating but not convergent C. Convergent but not absolutely convergent D. absolutely convergent?
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The series Sigma n=1 dask to infinity (-1)^n/2n+1 is A. not alternatin...
Convergence of the Series
• The given series is an alternating series because it alternates between positive and negative terms.
• The alternating series test states that if the terms of an alternating series decrease in absolute value and tend towards zero, then the series converges.
Absolute Convergence
• In this case, the series is (-1)^n / (2n + 1).
• If we take the absolute value of each term, we get 1 / (2n + 1), which does not tend towards zero as n approaches infinity.
• Therefore, the series is not absolutely convergent.
Convergence
• Despite not being absolutely convergent, the alternating series (-1)^n / (2n + 1) still converges by the Alternating Series Test.
• The terms of the series decrease in absolute value as n increases, and they approach zero.
• As a result, the series converges.
Final Verdict
• The given series is convergent but not absolutely convergent.
• Therefore, the correct answer is C. Convergent but not absolutely convergent.
• The given series is an alternating series because it alternates between positive and negative terms.
• The alternating series test states that if the terms of an alternating series decrease in absolute value and tend towards zero, then the series converges.
Absolute Convergence
• In this case, the series is (-1)^n / (2n + 1).
• If we take the absolute value of each term, we get 1 / (2n + 1), which does not tend towards zero as n approaches infinity.
• Therefore, the series is not absolutely convergent.
Convergence
• Despite not being absolutely convergent, the alternating series (-1)^n / (2n + 1) still converges by the Alternating Series Test.
• The terms of the series decrease in absolute value as n increases, and they approach zero.
• As a result, the series converges.
Final Verdict
• The given series is convergent but not absolutely convergent.
• Therefore, the correct answer is C. Convergent but not absolutely convergent.
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The series Sigma n=1 dask to infinity (-1)^n/2n+1 is A. not alternating B. alternating but not convergent C. Convergent but not absolutely convergent D. absolutely convergent?
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The series Sigma n=1 dask to infinity (-1)^n/2n+1 is A. not alternating B. alternating but not convergent C. Convergent but not absolutely convergent D. absolutely convergent? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The series Sigma n=1 dask to infinity (-1)^n/2n+1 is A. not alternating B. alternating but not convergent C. Convergent but not absolutely convergent D. absolutely convergent? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The series Sigma n=1 dask to infinity (-1)^n/2n+1 is A. not alternating B. alternating but not convergent C. Convergent but not absolutely convergent D. absolutely convergent?.
The series Sigma n=1 dask to infinity (-1)^n/2n+1 is A. not alternating B. alternating but not convergent C. Convergent but not absolutely convergent D. absolutely convergent? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The series Sigma n=1 dask to infinity (-1)^n/2n+1 is A. not alternating B. alternating but not convergent C. Convergent but not absolutely convergent D. absolutely convergent? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The series Sigma n=1 dask to infinity (-1)^n/2n+1 is A. not alternating B. alternating but not convergent C. Convergent but not absolutely convergent D. absolutely convergent?.
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