12. Power Series

Differentiation And Integration Of Power Series — Quiz

Test your understanding of differentiation and integration of power series with 5 practice questions.

Practice Questions

Question 1

If $f(x)=\sum_{n=0}^\infty a_n x^n$, what is the term-by-term derivative $f'(x)$?

Question 2

A power series converges for $|x-c|<R$. After differentiating or integrating term by term, what is the new radius of convergence?

Question 3

For $|x|<1$, what function is represented by $\sum_{n=0}^\infty \frac{x^{n+1}}{n+1}$?

Question 4

Differentiate the power series $\sum_{n=1}^\infty \frac{x^n}{n}$ term by term. What series do you get?

Question 5

For $|x|<1$, the series $\sum_{n=0}^\infty \frac{(-1)^n x^{2n+1}}{2n+1}$ represents which function?