What is a p-series?

 Learning objectives. 

1) Define what a p-series is?

2)  Determine if a p-series converges or diverges

Definition

For any real number p, the series 

is called a p-series. As examples the following harmonic series are p series:

Convergence and divergence 

A p-series converges if p>1 and diverges if p≤1

Examples

Determine if each of the following series converges or converges:

Solution

a) Here we have p>1 or 4>1. Therefore the series converges

b) p≤1 or 2/3≤1. The series diverges.

Practice

Determine if the following series:

converges or diverges.