chillywilly12a

2021-03-02

Use the Alternating Series Test, if applicable, to determine the convergence or divergence of the series.

$\sum _{n=1}^{\mathrm{\infty}}\frac{(-1{)}^{n}}{{n}^{5}}$

Margot Mill

Skilled2021-03-03Added 106 answers

The given series is

To check its convergence or divergence using Alternating series test.

Solution:

The alternating series says that if we have series of form,

1)

2)

Since we have series

Now to check both the condition using alternating series test for convergence,

1)

2)

So

Since , both the condition are satisficed so the given series is convergent.

Hence, the given series

Jeffrey Jordon

Expert2021-12-26Added 2605 answers

Answer is given below (on video)

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