MAT 302 Assignment Problem 9.1

MAT 302 Assignment Problem 9.1 | Borough of Manhattan Community College

9.1 Sequences

Question 1

(1 point) List the first five terms of the sequence:

Question 2

(1 point) List the first five terms of the sequence:

Question 3

Calculate the first four terms of the following sequence, starting with n=1n=1.

Question 4

Question 5

(1 point) Find a formula for the general term anan of the sequence (starting with a1a1):

Question 6

1 point) For each sequence, find a formula for the general term, anan. For example, answer n2n2 if given the sequence:
1,4,9,16,25,36,...

Question 7

(1 point) Answer the following questions about the sequence

Question 8

(1 point) Answer the following questions about the sequence

an=cosn.

Question 9

(1 point) Determine whether the following sequences converge or diverge. Answer "Converges" or "Diverges."

Question 10

(1 point) Find the limit of the sequence an=4n√1+7n√.an=4n1+7n. If the limit does not exist, type "Diverges" or "D".

Question 11

(1 point) Find the limit of the sequence an=(4n+1)!(4n−1)!.an=(4n+1)!(4n−1)!. If the limit does not exist, type "Diverges" or "D".

Question 12

(1 point) Find the limit of the sequence an=ln(9n+7)−lnn.an=ln⁡(9n+7)−ln⁡n. If the limit does not exist, type "Diverges" or "D".

Question 13

(1 point) Find the limit of the sequence an=(−1)n−1n6n2+1.an=(−1)n−1n6n2+1. If the limit does not exist, type "Diverges" or "D".

Question 14

(1 point) For each of the sequences below, enter either diverges if the sequence diverges, or the limit of the sequence if the sequence converges as n→∞n→∞. (Note that to avoid this becoming a "multiple guess" problem you will not see partial correct answers.)

Question 15

(1 point) For each of the sequences below, enter either diverges if the sequence diverges, or the limit of the sequence if the sequence converges as n→∞n→∞. (Note that to avoid this becoming a "multiple guess" problem you will not see partial correct answers.)

Question 16

Determine the limit of the sequence or show that the sequence diverges by using the appropriate Limit Laws or theorems. If the sequence diverges, enter DIV as your answer.
Note: Show your work on paper. Your instructor may choose to collect it.

Question 17

Determine the limit of the sequence or show that the sequence diverges by using the appropriate Limit Laws or theorems. If the sequence diverges, enter DIV as your answer.
Note: Show your work on paper. Your instructor may choose to collect it.

Question 18

(1 point) Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as INF. If it diverges to negative infinity, state your answer as MINF. If it diverges without being infinity or negative infinity, state your answer as DIV.

Q uestion 19

(1 point) Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as INF. If it diverges to negative infinity, state your answer as MINF. If it diverges without being infinity or negative infinity, state your answer as DIV.

Q uestion 20

(1 point) Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.

(If it diverges to infinity, state your answer as inf . If it diverges to negative infinity, state your answer as -inf . If it diverges without being infinity or negative infinity, state your answer as div .)

Q uestion 21

(1 point) Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.

(If it diverges to infinity, state your answer as inf . If it diverges to negative infinity, state your answer as -inf . If it diverges without being infinity or negative infinity, state your answer as div .

Q uestion 22

(1 point) Determine whether the following sequences converge or diverge. Answer "Converges" or "Diverges."