Question

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

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

Answer 1

Multiplying 60 by what fraction results in -10?
Multiplying -10 bye what fraction results in 5/3?
Multiplying 5/3 by what fraction results in -5/18?
What would happen if we took any one of these terms (-10, 5/3,-5/18, etc.), multiply it by (the fraction you've just found)^n, and then let n approach infinity?

Answer 2

1/-6

Answer 3

great. I'd prefer to see (-1/6) or just -1/6, but 1/-6 is nevertheless correct.
Can you now find the limit as n approaches infinity of (5/3)(-1/6)^n?

Answer 4

i have no idea how to do that part ahah, but if its approaching infinity doesn't it diverge? @mathmale

Answer 5

Try evaluating (-1/6)^1, (-1/6)^2, (-1/6)^3, and so on. What about (-1/6)^100? (-1/6)^1000? If n approaches infinity, what value would (-1/6) n approach? Use a calculator if you have one.

Answer 6

ok

Answer 7

it gets closer and closer to 0 @mathmale

Answer 8

so that means it converges to 0?