# Determine whether the series \sum_{n=1}^{\infty} 9n^{-0.5} converges or diverges, Identify the...

## Question:

Determine whether the series {eq}\sum_{n=1}^{\infty} 9n^{-0.5} {/eq} converges or diverges, Identify the test used

## P-Series Test:

A p-series is a series in the general form {eq}\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^p} {/eq} where p is a constant real number. A p-series converges if and only if p is larger than 1.

This result can be proven by using the integral test and the divergence test.

## Answer and Explanation: 1

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We have a p-series {eq}\displaystyle \sum_{n=1}^{\infty} 9n^{-0.5} = \sum_{n=1}^{\infty} \frac{9}{n^{0.5}} = \sum_{n=1}^{\infty} \frac{9}{n^{...

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#### Learn more about this topic: 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.