Use the Alternating Series Test, if applicable, to determine the convergence or divergence of the series. sum_{n=2}^inftyfrac{(-1)^nn}{n^2-3}

sibuzwaW

sibuzwaW

Answered question

2020-10-25

Use the Alternating Series Test, if applicable, to determine the convergence or divergence of the series.
n=2(1)nnn23

Answer & Explanation

rogreenhoxa8

rogreenhoxa8

Skilled2020-10-26Added 109 answers

We have given series
n=2(1)nnn23
Let, n=2(1)nan=n=2(1)nnn23
Then, an=nn23
an+1=n+1(n+1)23
limnan=limnnn23
=limnnn2(13n2)
=0
n23<(n+1)23
1n23>1(n+1)23
nn23>n(n+1)23
an>an+1
Therefore, sequence {an} is decreaing.
So, by alternating series test given series is convergent.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-16Added 2605 answers

Answer is given below (on video)

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