Question

Determine whether the sequence converges or diverges. If it converges, give the limit.

a. Diverges
b. Converges; 11100
c. Converges; 72
d. Converges; 0

60, -10, 5/3, -5/18

Answer 1

1080, -180, 30, -5
------------------
18

well, the pattern seems to be wobbling back and forth between signs and getting smaller and smaller

since they are bobbling back and forth, lets just absolute value it

1080, 180, 90, 5
---------------
18

can we define a expression for the top sequence?

ince this is clearly not arithmetic ....dividing by 5 we get

{1080, 180, 90, 5}/5 = { 216, 36, 18, 1}

divide by 6: 36, 6 ,3 ,1/6

divide by 3: 12, 2 ,1 ,1/18

divide by 2: 6, 1 ,1/2 ,1/36

divide by 6: 1, 1/6 ,1/12 ,1/236

in some fashion or another the top is approaching 0

60/6 = 10

10/6 = 5/3

(5/3)/6 = 5/18

its a geometric series

since |-1/6| < 1 .... it goes to zero

60*0 = 0

Answer 2

Thank you :) @gurrilabill

Answer 3

no problem :)