# Determine if the following series is convergent or divergent. Sum of 1/(n^(2/3)) from n = 1 to...

## Question:

Determine if the following series is convergent or divergent.

{eq}\sum_{n=1}^{\infty} \frac{1}{n^{\frac{2}{3}}} {/eq}

## P-Series Test:

A series in the general form {eq}\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^p} {/eq} is called a p-series.

By using the integral test and the divergence test one can show that this series converges if and only if p is larger than 1.

## Answer and Explanation:

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We have a p-series {eq}\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^{\frac{2}{3}}} \; {/eq} with {eq}\displaystyle \; p = \frac{2}{3}...

See full answer below.

P-Series: Definition & Examples

from

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.