10. Infinite Sequences and Series

Ratio Test For Convergence — Quiz

Test your understanding of ratio test for convergence with 5 practice questions.

Practice Questions

Question 1

What does the Ratio Test say when a series with terms $a_n$ has $L=\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|$ and $L<1$?

Question 2

For the series $\sum_{n=1}^{\infty}\frac{1}{n}$, what is the value of $\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|$?

Question 3

Use the Ratio Test for the series $\sum_{n=1}^{\infty}\frac{n}{2^n}$. What conclusion is correct?

Question 4

For the series $\sum_{n=1}^{\infty}\frac{2^n}{n!}$, what is the limit $\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|$?

Question 5

What does the Ratio Test conclude when $L=\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|=1$?