All Convergence Tests

Which of the following tests would be the best choice to prove the series is divergent?

• nth term test

• integral test

• direct comparison test

• limit comparison test

What is the sum of the series?

• -4/3

• 2/3

• 9/2

• the series diverges

Which of the following is true about the given series?

• it is a divergent p-series

• it is a convergent p-series

• it is a divergent geometric series

• it is a convergent geometric series

Which test can NOT be used to prove that the series diverges?

• limit comparison test

• direct comparison test

• p-series

• integral test

Select the correct comparison series you would use for the given series.

• $\Sigma\ \frac{1}{n}$

• $\Sigma\ \frac{1}{n^2}$

• $\Sigma\ \left(\frac{1}{2}\right)^n$

• $\Sigma\ \left(2\right)^n$

Select the correct limit if you used the limit comparison test to prove the series converges.

• $\lim_{n\rightarrow\infty}\ \frac{n^4}{n^3+2}=\infty$

• $\lim_{n\rightarrow\infty}\ \frac{n}{n^3+2}=0$

• $\lim_{n\rightarrow\infty}\ \frac{n^3}{n^3+2}=1$

• The series diverges

Tags

CCSS.HSA.APR.D.7

Which of the following is true about the alternating series?

• It is conditionally convergent

• It is absolutely convergent

• It is divergent

What is the result of the limit when using the ratio test on the series?

• 0

• 1/2

• 1

• 2

What test would be used, and what is the result of the test?

• limit comparison, diverge

• alternating series, conditionally converge

• geometric series, diverge

• p-series, converge

What would be the test used, and what is the result of the test?

• alternating series, diverge

• alternating series, conditionally converge

• ratio test, converge

• geometric series, diverge