Which of the series, and which diverge? Give reasons for your answers. (When you check an answer, remember that there may be more than one way to determine the series’ convergence or divergence.) sum_{n=1}^inftyfrac{1}{2n-1}

babeeb0oL 2020-10-28 Answered
Which of the series, and which diverge?
Give reasons for your answers. (When you check an answer, remember that there may be more than one way to determine the series’ convergence or divergence.)
n=112n1
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Expert Answer

au4gsf
Answered 2020-10-29 Author has 95 answers
The given series is
n=112n1
Use Limit Comparison Test to find whether the given series is convergent or divergent.
The nth term of series is
an=12n1
Consider a series
n=1Bn=n=11n
then, Bn=1n
Now,
limn(anBn)=limn(12n11n)
limn(n2n1)
=limn(nn(21n))
=limn(121n)
=12>0
Since, series {Bn} is divergent.
Therefore, the given series is also divergent.
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Jeffrey Jordon
Answered 2021-12-16 Author has 2064 answers

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