# Divergence test

### Divergence test

In this lesson, we will learn about the divergence test. The test states that if you take the limit of the general term of the series and it does not equal to 0, then the series diverge. Keep in mind that if you do take the limit and it goes to 0, that does not mean the series is convergent. It only means the test has failed, and you will have to use another method to find the convergence or divergence of the series. It is recommended to use the divergence test if u can obviously see that the limit of the general term goes to infinity. For the first few questions, we will see if the divergence test applies to the series. For the last question, we will see if the series is convergent or divergent by using the test.

#### Lessons

Note *The divergence test states the following:
If $\lim$n →$\infty$ $a$$n$ $\neq$ 0, then the series $\sum a_n$ diverges.
• Introduction
Divergence Test Overview

• 1.
Understanding of the Divergence Test
Does the divergence test work for the following series?
a)
$\sum_{n=1}^{\infty}\frac{10}{n}$

b)
$\sum_{n=4}^{\infty}\frac{n^2+n^3}{n^3+1}$

c)
$\sum_{n=2}^{\infty}\frac{n-1}{ln(n)}$

• 2.
Advanced Question Regarding to the Divergence Test
Determine if the series $\sum_{k=1}^{\infty}k^{-\frac{1}{k^3}}$ converges or diverges.