Use the Alternating Series Test, if applicable, to determine the convergence or divergence of the series. sum_{n=1}^inftyfrac{(-1)^n}{n^5}

chillywilly12a

chillywilly12a

Answered question

2021-03-02

Use the Alternating Series Test, if applicable, to determine the convergence or divergence of the series.
n=1(1)nn5

Answer & Explanation

Margot Mill

Margot Mill

Skilled2021-03-03Added 106 answers

The given series is n=1(1)nn5
To check its convergence or divergence using Alternating series test.
Solution:
The alternating series says that if we have series of form, n=1(1)nbn, then if,
1)limnbn=0 and
2)bn is a decreasing sequence, then the series n=1(1)nbn is said to be convergent.
Since we have series n=1(1)nn5 we have sequence bn as bn=1n5,
Now to check both the condition using alternating series test for convergence,
1) limnbn=limn1n5=0
2) n5<(n+1)5
1n5>1(n+1)5
bn>bn+1
So bn is the decreasing sequence as well,
Since , both the condition are satisficed so the given series is convergent.
Hence, the given series n=1(1)nn5 is convergent.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-26Added 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?