1. Pure Algebra

Sequences Series — Quiz

Test your understanding of sequences series with 5 practice questions.

Practice Questions

Question 1

Which of the following expressions correctly represents the finite sum $\sum_{k=1}^n k\,r^{k-1}$ for $r\neq1$?

Question 2

Evaluate the infinite series $\displaystyle\sum_{k=1}^\infty \frac{k}{2^{k-1}}$.

Question 3

Using the ratio test, determine whether the series $\sum_{n=1}^\infty \frac{n!}{n^n}$ converges or diverges.

Question 4

Which formula gives the finite sum $\sum_{k=1}^n k\,r^k$ for $r\neq1$?

Question 5

Given the partial sums $S_n=5-2^{-n}$ of a series, what is the general term $u_n$ and the sum to infinity?