Which of the following?

Question

Which of the following is the limit of the sequence with nth term an=(-1)^n*(3n-1)/(n+2)? 

 

a) -3

b) 0

c) 2

d) 3

e) diverges

 

Please show all your work. 

Answer 1

Use alternate series test

 

Disregard (-1)ⁿ for a second

 

Lim as n  > infinity of (3n-1)/(n+2) is 3 

 

so conclusion by alternative series test is: you cannot conclude it converges because the lim as n  > infinity does NOT equal zero

 

by nth term test do

 

lim as n > infinity

 

does not equal zero so diverges

 

Answer is E. Diverges