10. Convergence Tests I

Comparison Tests — Quiz

Test your understanding of comparison tests with 5 practice questions.

Practice Questions

Question 1

Which statement correctly describes the direct comparison test for series with nonnegative terms?

Question 2

Does the series $\sum_{n=1}^{\infty} \frac{1}{n^2+3}$ converge or diverge?

Question 3

Using comparison with the harmonic series, what can be concluded about $\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}$?

Question 4

Does the series $\sum_{n=1}^{\infty} \frac{n}{n^3+1}$ converge or diverge?

Question 5

If $\lim_{n\to\infty} \frac{a_n}{b_n} = 5$ and $\sum b_n$ converges, what happens to $\sum a_n$?