10. Convergence Tests I

Integral Test — Quiz

Test your understanding of integral test with 5 practice questions.

Practice Questions

Question 1

Which set of conditions must $f(x)$ satisfy on $[N,\infty)$ before the Integral Test can be used for the series $\sum_{n=N}^\infty a_n$ with $a_n=f(n)$?

Question 2

Since $f(x)=\frac{1}{x^2}$ is positive, continuous, and decreasing on $[1,\infty)$, what does the convergence of $\int_1^\infty \frac{1}{x^2}\,dx$ imply about $\sum_{n=1}^\infty \frac{1}{n^2}$?

Question 3

What is the exact value of $\int_1^\infty \frac{1}{x^2}\,dx$?

Question 4

Using the Integral Test, what happens to the series $\sum_{n=1}^\infty \frac{1}{n}$?

Question 5

Using the Integral Test, what happens to the series $\sum_{n=2}^\infty \frac{1}{n\ln n}$?