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

babeeb0oL

Answered question

2020-10-28

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

Answer & Explanation

au4gsf

au4gsf

Skilled2020-10-29Added 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.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-16Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?