Question 1

Which of the following is the correct application of the limit comparison test when analyzing the convergence of the series

\sum a_n

given the series

\sum b_n

?

Accepted Answer

If

\sum a_n

, where

\sum b_n

, then both series either converge or diverge.

Answer

If

\sum a_n

, where

\sum b_n

, then both series either converge or diverge.

Answer

If

\sum a_n

, then only

\sum b_n

converges.

Answer

If

\sum a_n

, then only

\sum b_n

converges.

Question 2

Given the series

\sum a_n

, which comparison could be used to determine its convergence using the limit comparison test?

Accepted Answer

Compare with the series

\sum a_n

.

Answer

Compare with the series

\sum a_n

.

Answer

Compare with the series

\sum a_n

.

Answer

Compare with the series

\sum a_n

.

Question 3

For which values of

\sum a_n

does the limit comparison test indicate convergence of the series

\sum b_n

by comparing it to

\sum_{n=1}^{\infty} \frac{1}{n^p}

?

Accepted Answer

The series converges for

\sum a_n

.

Answer

The series converges for

\sum a_n

.

Answer

The series converges for

\sum a_n

.

Answer

The series converges for

\sum a_n

.

Question 4

Which of the following statements correctly applies the limit comparison test to determine the convergence of the series

\sum a_n

?

Accepted Answer

Compare with the series

\sum a_n

; since

\sum b_n

, both series converge.

Answer

Compare with the series

\sum a_n

; since

\sum b_n

, both series converge.

Answer

Compare with the series

\sum a_n

; since

\sum b_n

, both series converge.

Answer

Compare with the series

\sum a_n

; since

\sum b_n

, both series diverge.

Question 5

Determine which series should be used in the limit comparison test to analyze the convergence of

\sum a_n

.

Accepted Answer

Compare with the series

\sum a_n

.

Answer

Compare with the series

\sum a_n

.

Answer

Compare with the series

\sum a_n

.

Answer

Compare with the series

\sum a_n

.

Question 6

Which comparison would be valid using the limit comparison test for the series

\sum a_n

?

Accepted Answer

Compare with the series

\sum a_n

.

Answer

Compare with the series

\sum a_n

.

Answer

Compare with the series

\sum a_n

.

Answer

Compare with the series

\sum a_n

.

Question 7

Given the series

\sum a_n

, which of the following series can be used for comparison using the Limit Comparison Test?

Accepted Answer

\sum_{n=1}^{\infty} \frac{1}{n^2}

Answer

\sum_{n=1}^{\infty} \frac{1}{n^2}

Answer

\sum_{n=1}^{\infty} \frac{1}{n^2}

Answer

\sum_{n=1}^{\infty} \frac{1}{n^2}

Question 8

For which constant

\sum a_n

does the series

\sum b_n

suggest using the limit comparison test with the series

\sum_{n=1}^{\infty} \frac{1}{n^p}

?

Accepted Answer

\sum_{n=1}^{\infty} \frac{1}{n^2}

Answer

\sum_{n=1}^{\infty} \frac{1}{n^2}

Answer

\sum_{n=1}^{\infty} \frac{1}{n^2}

Answer

\sum_{n=1}^{\infty} \frac{1}{n^2}

Question 9

Determine the convergence or divergence of the series sum from n=1 to infinity of

\sum a_n

using the limit comparison test.

Accepted Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which diverges

Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which converges

Answer

Use the integral test

Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which converges

Question 10

Use the limit comparison test to determine the convergence or divergence of the series sum from n=1 to infinity of

\sum a_n

.

Accepted Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which diverges

Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which diverges

Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which converges

Answer

Use the p-series test

Question 11

Determine the convergence or divergence of the series sum from n=1 to infinity of

\sum a_n

using the limit comparison test.

Accepted Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which converges

Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which diverges

Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which diverges

Answer

Use the p-series test

Question 12

Apply the limit comparison test to determine the convergence or divergence of the series sum from n=1 to infinity of

\sum a_n

.

Accepted Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which converges

Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which diverges

Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which diverges

Answer

Use the integral test

Question 13

Use the limit comparison test to determine if the series sum from n=1 to infinity of

\sum a_n

converges or diverges.

Accepted Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which diverges

Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which diverges

Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which converges

Answer

Use the ratio test

Question 14

Determine the convergence or divergence of the series sum from n=1 to infinity of

\sum a_n

using the limit comparison test.

Accepted Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which diverges

Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which diverges

Answer

Compare with the series sum from n=1 to infinity of

\sum a_n

which converges

Answer

Use the integral test

Question 15

Using the limit comparison test, determine if the series sum from n=2 to infinity of

\sum a_n

converges or diverges.

Accepted Answer

Compare with the series sum from n=2 to infinity of

\sum a_n

which diverges

Answer

Compare with the series sum from n=2 to infinity of

\sum a_n

which converges

Answer

Compare with the series sum from n=2 to infinity of

\sum a_n

which converges

Answer

Use the ratio test

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