10. Infinite Sequences and Series

Radius And Interval Of Convergence Of Power Series — Quiz

Test your understanding of radius and interval of convergence of power series with 5 practice questions.

Practice Questions

Question 1

For the power series $\sum_{n=0}^{\infty} x^n$, what is the interval of convergence?

Question 2

For the power series $\sum_{n=1}^{\infty} \frac{x^n}{n}$, what is the interval of convergence?

Question 3

A power series has radius of convergence $R=3$. What does this guarantee about the series?

Question 4

For the series $\sum_{n=0}^{\infty} n!\,x^n$, what is the radius of convergence?

Question 5

Which statement about endpoints of a power series interval of convergence is correct?