5. Series

Convergence Tests — Quiz

Test your understanding of convergence tests with 5 practice questions.

Practice Questions

Question 1

According to the $n$th-term test for divergence, if $\lim_{n\to\infty} a_n \neq 0$, what must be true about $\sum_{n=1}^{\infty} a_n$?

Question 2

What is the value of $\sum_{n=0}^{\infty}\left(\frac{1}{2}\right)^n$?

Question 3

The p-series test says that $\sum_{n=1}^{\infty}\frac{1}{n^p}$ converges when...

Question 4

The series $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n}$ is...

Question 5

If $\sum_{n=1}^{\infty}|a_n|$ converges, what can be concluded about $\sum_{n=1}^{\infty}a_n$?