# Determine if the p-series converges or diverges. sum n = 1 infty 1 n 22

## Question:

Determine if the p-series converges or diverges.

{eq}\sum \limits_{n = 1}^{\infty} \frac{1}{n^{22}} {/eq}

## p-Series:

A p-series is any series that follows the standard form:

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

The p-series is named for its exponent p, which determines its convergence. As long as p is greater than 1.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer! Create your account

Given the series:

{eq}\displaystyle \rm \sum\limits_{n = 1}^\infty \frac{1}{n^{22}} {/eq}

This is a standard p-series of the form:

{eq}\displays...

See full answer below.

#### Learn more about this topic: P-Series: Definition & Examples

from

Chapter 29 / Lesson 5
23K

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.