The Root Test

 Objectives:

1) Define the root test

2) Use the root test to determine if a series converges or diverges

Definition

The ratio test uses the limit of the square root of the absolute value of a series to determine its convergence or divergence. It is used in series involving exponentials.

Theorem 

Examples

Solutions

a. Let's determine ρ:

Since ρ<1, the series converges absolutely.

b. Let's determine p:

ρ = ∞/∞ (indetermination)

Let's get rid of the indetermination by applying the l'Hospital rule:

The series diverges.

Practice