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The series 
- a)conditional convergent
- b)absolutely convergent
- c)divergent
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The seriesa)conditional convergentb)absolutely convergentc)divergentd)...
Let the given series be denoted by ∑μn, then
∑|μn|
Compare this series ∑vn with the auxiliary series,
Then,
which is finite quantity.
Hence, ∑un and ∑wn are either both convergent or both divergent. But ∑wn
Hence, the series ∑vn is divergent.
Also, in the series ∑un, we find that its term are alternately positive and negative, its terms are continuously decreasing and
Thus, all condition of Leibnitz’s test are satisfied and as such ∑un is convergent. H ence, the given series ∑un is conditionally convergent.
∑|μn|
Compare this series ∑vn with the auxiliary series,
Then,
which is finite quantity.
Hence, ∑un and ∑wn are either both convergent or both divergent. But ∑wn
Hence, the series ∑vn is divergent.
Also, in the series ∑un, we find that its term are alternately positive and negative, its terms are continuously decreasing and
Thus, all condition of Leibnitz’s test are satisfied and as such ∑un is convergent. H ence, the given series ∑un is conditionally convergent.
Most Upvoted Answer
The seriesa)conditional convergentb)absolutely convergentc)divergentd)...
Here ,the given series is of positive terms and therefore the series will be Divergent.
so, option (c) is correct
so, option (c) is correct
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Community Answer
The seriesa)conditional convergentb)absolutely convergentc)divergentd)...
In the above we have used the result that 1/n → 0 as n → ∞ and a result about combining convergent sequences and noting that the denominator converges to a non-zero value.
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The seriesa)conditional convergentb)absolutely convergentc)divergentd)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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The seriesa)conditional convergentb)absolutely convergentc)divergentd)None of the aboveCorrect answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The seriesa)conditional convergentb)absolutely convergentc)divergentd)None of the aboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The seriesa)conditional convergentb)absolutely convergentc)divergentd)None of the aboveCorrect answer is option 'A'. Can you explain this answer?.
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