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Determine if the p-series converges or diverges. n = 1 1 4 n 3

Question:

Determine if the p-series converges or diverges.

{eq}\displaystyle \sum_{n=1}^\infty \frac{1}{\sqrt[4]{n^3}}{/eq}

p-Series:

A p-series is an infinite series that can be written in the form:

{eq}\displaystyle \sum_{n=1}^\infty \frac{1}{n^p} {/eq}

We can check for the convergence of a p-series simply by looking at the exponent p. If {eq}\displaystyle p > 1 {/eq}, the series is convergent.

Answer and Explanation: 1

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We are given:

{eq}\displaystyle \sum_{n=1}^\infty \frac{1}{\sqrt[4]{n^3}} {/eq}

We can rewrite this series as:

{eq}\displaystyle...

See full answer below.


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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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