10. Infinite Sequences and Series

Representing Functions As Power Series — Quiz

Test your understanding of representing functions as power series with 5 practice questions.

Practice Questions

Question 1

Which function is represented by the power series $\sum_{n=0}^{\infty} x^n$ for $|x|<1$?

Question 2

Which function is represented by the power series $\sum_{n=0}^{\infty} (-1)^n x^n$ for $|x|<1$?

Question 3

Which function is represented by the power series $\sum_{n=0}^{\infty} \left(\frac{x}{2}\right)^n$ for $|x|<2$?

Question 4

Which function is represented by the power series $\sum_{n=0}^{\infty} x^{2n}$ for $|x|<1$?

Question 5

Which function is represented by the power series $\sum_{n=0}^{\infty} 3(-x)^n$ for $|x|<1$?