# Determine if the following series converges or diverges. \displaystyle...

## Question:

Determine if the following series converges or diverges.

{eq}\displaystyle \frac{\sqrt{1}}{1}+\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{3}+\frac{\sqrt{4}}{4}+\cdots {/eq}

## P-Series Test:

A series in the form {eq}\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^p} {/eq} with p, a constant real number, is called a p-series. Such a series converges if the exponent p> 1 and otherwise diverges to positive infinity.

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We have {eq}\displaystyle \; \frac{\sqrt{1}}{1}+\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{3}+\frac{\sqrt{4}}{4}+\cdots = \sum_{n=1}^{\infty} \frac{\sqrt...

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.