Mathematics Exam > Mathematics Questions > The seriesa)conditional convergentb)absolutel...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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
Free Test
FREE
| Start Free Test |
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.
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
The seriesa)conditional convergentb)absolutely convergentc)divergentd)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
Question Description
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?.
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?.
Solutions for The seriesa)conditional convergentb)absolutely convergentc)divergentd)None of the aboveCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of The seriesa)conditional convergentb)absolutely convergentc)divergentd)None of the aboveCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The seriesa)conditional convergentb)absolutely convergentc)divergentd)None of the aboveCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for The seriesa)conditional convergentb)absolutely convergentc)divergentd)None of the aboveCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of The seriesa)conditional convergentb)absolutely convergentc)divergentd)None of the aboveCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The seriesa)conditional convergentb)absolutely convergentc)divergentd)None of the aboveCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup