Determine whether the series is absolutely or conditionally convergent or divergent. \sum_{n =...

Question:

Determine whether the series is absolutely or conditionally convergent or divergent.

{eq}\sum_{n = 1}^{\infty} \frac{(-1)^n}{ \sqrt {n^3}} {/eq}

Absolute Convergence:

A series whose terms are alternately {eq}+ve {/eq} and {eq}-ve {/eq} is called an alternating series.

We apply the tests for convergence to the series of absolute values of an alternating series.

A series {eq}\sum a_{n} {/eq} converges absolutely if {eq}\sum \left | a_{n} \right | {/eq} converges.

Answer and Explanation:

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Let {eq}a_{n}=\frac{\left ( -1 \right )^{n}}{\sqrt{n^3}} {/eq}.

Then {eq}\left | a_{n} \right |=\frac{1}{n^{\frac{3}{2}}} {/eq}

{eq}\Rightarrow...

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P-Series: Definition & Examples

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Chapter 29 / Lesson 5
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This lesson is designed to help you understand a specific type of series called a p-series. You will determine if a series is a p-series, and you will learn to decide if a p-series converges or diverges.


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