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Let ∑un be a series of positive terms such that  Then,

(i) if l > 1, the series converges;

(ii) if l < 1, the series diverges;

(iii) if l = 1, the series may either converge or diverge and therefore the test fails;

​This theorem is known as

  • a)
    Raabe’s test

  • b)
    Cauchy test

  • c)
    d’Alembert’s tes

  • d)
    Kummer’s test

Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let ∑un be a series of positive terms such thatThen,(i) if l> 1...
Correct Answer :- A
Explanation : The series for Rabee’s test is :
Converge when there exists a c>1 such that l is greater than and equal to c for all n>N.
Diverge when l is less than and equal to 1 for all n>N.
Otherwise, the test is inconclusive.
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Most Upvoted Answer
Let ∑un be a series of positive terms such thatThen,(i) if l> 1...
Correct answer is C . rabbe's test is applicable for infinite series when ' D ' alembert ratio test fail.
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Community Answer
Let ∑un be a series of positive terms such thatThen,(i) if l> 1...
Correct Answer :- A
Explanation : The series for Rabee’s test is :
Converge when there exists a c>1 such that l is greater than and equal to c for all n>N.
Diverge when l is less than and equal to 1 for all n>N.
Otherwise, the test is inconclusive.
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Let ∑un be a series of positive terms such thatThen,(i) if l> 1, the series converges;(ii)if l< 1, the series diverges;(iii) if l = 1, the series may either converge or diverge and therefore the test fails;This theorem is known asa)Raabe’s testb)Cauchy testc)d’Alembert’s tesd)Kummer’s testCorrect answer is option 'A'. Can you explain this answer?
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