11. Convergence Tests II

Root Test — Quiz

Test your understanding of root test with 5 practice questions.

Practice Questions

Question 1

In the root test for a series $\sum a_n$, which quantity is examined?

Question 2

If $L=\lim_{n\to\infty}\sqrt[n]{|a_n|}$ satisfies $L<1$, what does the root test conclude?

Question 3

Compute $L=\lim_{n\to\infty}\sqrt[n]{\frac{n}{2^n}}$.

Question 4

Use the root test on the series $\sum \left(\frac{3}{4}\right)^n$. What is the correct conclusion?

Question 5

Use the root test on the series $\sum 2^n$. What conclusion follows?