Chapter 10.4, Problem 45E

To determine

To Explain: the converse of the nth term test is false with an example.

Answer to Problem 45E

  ${\displaystyle \sum _{n=0}^{\infty }\frac{1}{n}}$ is an example

Explanation of Solution

Example:

  ${\displaystyle \sum _{n=0}^{\infty }{a}_n}={\displaystyle \sum _{n=0}^{\infty }\frac{1}{n}}$ is divergent

  $\underset{n\to \infty }{\lim }{a}_n=\underset{n\to \infty }{\lim }\frac{1}{n}=0$ which is less than 1