6. Series and Sequences

Power Series — Quiz

Test your understanding of power series with 5 practice questions.

Practice Questions

Question 1

What is the interval of convergence for the power series $\sum_{n=0}^{\infty} \frac{(x-1)^n}{n}$?

Question 2

For the power series $\sum_{n=1}^{\infty} \frac{(x-3)^n}{n^2}$, what can be said about the convergence at $x=4$?

Question 3

What is the power series representation for the function $f(x) = \frac{1}{1+x}$ centered at $x=0$?

Question 4

Given the power series $\sum_{n=0}^{\infty} \frac{(x-2)^n}{n!}$, what is its radius of convergence?

Question 5

What happens to the radius of convergence when a power series is differentiated term-by-term?