MAT 302 Assignment Problem 9.6

MAT 302 Assignment Problem 9.6 | Borough of Manhattan Community College

9.6 The Ratio and Root Test

Question 1

(1 point) What can you say about the series ∑an∑an in each of the following cases using the Ratio Test? Answer "Convergent," "Divergent," or "Inconclusive."

Question 2

(1 point) Use the ratio test to determine whether

converges or diverges.

(a)   Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n≥7n≥7,

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

(b)  By the ratio test, does the series converge, diverge, or is the test inconclusive?

Question 3

(1 point) Use the ratio test to determine whether 

converges or diverges.

(a)   Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n≥3n≥3,

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

(c)   By the ratio test, does the series converge, diverge, or is the test inconclusive?

Question 4

(1 point) Use the ratio test to determine whether 

converges or diverges.

(a)   Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n≥7n≥7,

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

(c)   By the ratio test, does the series converge, diverge, or is the test inconclusive? 

Note: You can earn 40% partial credit for 2 - 3 correct answers.

Question 5

(1 point) Consider the series 

Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it does not exist, type

What can you say about the series using the Ratio Test? Answer "Convergent", "Divergent", or "Inconclusive".

Question 6

(1 point) Consider the series 

Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it does not exist, type "DNE".

What can you say about the series using the Ratio Test? Answer "Convergent", "Divergent", or "Inconclusive".

Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent".

Note: In order to get credit for this problem all answers must be correct.

Question 7

(1 point) Consider the series 

Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it does not

exist, type "DNE".

What can you say about the series using the Ratio Test? Answer "Convergent", "Divergent", or "Inconclusive".

Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent".

Note: In order to get credit for this problem all answers must be correct.

Question 8

Use the Root Test to determine the convergence or divergence of the given series or state that the Root Test is inconclusive.

Question 9

(1 point) Consider the series 

Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it does not exist, type "DNE".

What can you say about the series using the Ratio Test? Answer "Convergent", "Divergent", or "Inconclusive".

Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent".

Question 10

(1 point) Consider the series 

 Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it does not exist, type

What can you say about the series using the Ratio Test? Answer "Convergent", "Divergent", or "Inconclusive".

Question 11

(1 point) Consider the series

Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it does not exist, type "DNE".

What can you say about the series using the Root Test? Answer "Convergent", "Divergent", or "Inconclusive".

Question 12

Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is inconclusive.

Question 13

Use the Root Test to determine the convergence or divergence of the given series or state that the Root Test is inconclusive.

Question 14

(1 point) Use the Root Test to determine the convergence or divergence of the series.
Enter CON for converge, DIV for diverge, and INC for inconclusive.

Question 15

(1 point) Consider the series

Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it does not exist, type "DNE".

What can you say about the series using the Root Test? Answer "Convergent", "Divergent", or "Inconclusive".

Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent".

Question 16

Use the Root Test to determine the convergence or divergence of the given series or state that the Root Test is inconclusive.

Question 17

Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is inconclusive.

Question 18

(1 point) Use the Root Test to determine the convergence or divergence of the series.
Enter CON for converge, DIV for diverge, and INC for inconclusive.