MAT 302 Assignment Problem 9.4

MAT 302 Assignment Problem 9.4 | Borough of Manhattan Community College

9.4 Comparisons of Series

Question 1

(1 point) Use the limit comparison test to determine whether 

 converges or diverges.

(a)   Choose a series ∑n=13∞bn∑n=13∞bn with terms of the form bn=1npbn=1np and apply the limit comparison test. Write your answer as a fully simplified

fraction. For n≥13n≥13,

(b)   (b) Evaluate the limit in the previous part. Enter ∞∞ as infinity and −∞−∞ as -infinity. If the limit does not exist, enter DNE.
limn→∞anbn

Ans b =9/4

(c)

 By the limit comparison test, does the series converge, diverge, or is the test inconclusive?

Question 2

(1 point) Use the limit comparison test to determine whether

converges or diverges.

(a)    Choose a series ∑n=3∞bn∑n=3∞bn with terms of the form bn=1npbn=1np and apply the limit comparison test. Write your answer as a fully simplified fraction. For n≥3n≥3,

Question 3

(1 point) Match the following series with the series below in which you can compare using the Limit Comparison Test. Then determine whether the series converge or diverge.

Question 4

(1 point) Use the Limit Comparison Test to determine the convergence or divergence of the series.
Enter D for divergence, C for convergence.

Question 5

(1 point) Match the following series with the series below in which you can compare using the Limit Comparison Test. Then determine whether the series converge or diverge.

Question 6

(1 point) The three series ∑An∑An, ∑Bn∑Bn, and ∑Cn∑Cn have terms

Use the Limit Comparison Test to compare the following series to any of the above series. For each of the series below, you must enter two letters. The first is the letter (A,B, or C) of the series above that it can be legally compared to with the Limit Comparison Test. The second is C if the given series converges, or D if it diverges. So for instance, if you believe the series converges and can be compared with series C above, you would enter CC; or if you believe it diverges and can be compared with series A, you would enter AD.

Question 7

(1 point) Match the following series with the series below in which you can compare using the Limit Comparison Test. Then determine whether the series converge or diverge.

Question 8

(1 point) Match the following series with the series below in which you can compare using the Limit Comparison Test. Then determine whether the series converge or diverge.

Question 9

(1 point) Match the following series with the series below in which you can compare using the Limit Comparison Test. Then determine whether the series converge or diverge.

Question 10

(1 point) Determine whether the following series converges or diverges:

Question 11

(1 point) Use the Direct Comparison Test to determine the convergence or divergence of the series.
Enter D for divergence, C for convergence.

Question 12

(1 point) Use the Direct Comparison Test to determine the convergence or divergence of the series.
Enter D for divergence, C for convergence.

Question 13

(1 point) Use the Direct Comparison Test to determine the convergence or divergence of the series.
Enter D for divergence, C for convergence.

uestion 14

(1 point) Use the Direct Comparison Test to determine the convergence or divergence of the series.
Enter D for divergence, C for convergence.

Question 15

(1 point) Determine whether the following series converges or diverges.