Question

(1/8)-(1/4)+(1/2)-1+.... divergent. but how can i proof it?

Answer 1

What is the common ratio of this geometric sequence?

Answer 2

(1/8)? I don't know

Answer 3

What do you multiply 1/8 by to get -1/4?
What do you multiply -1/4 by to get 1/2?
What do you multiply 1/2 by to get -1?

Answer 4

-2

Answer 5

Right :) So the common ratio is -2. Now there is a test that will show that a geometric sequence converges or diverges. It turns out you check the common ratio. Lets say the common ratio is r. (in your case, r = -2). If:\[|r|<1\]then your series converges. Otherwise it diverges.

Answer 6

btw, if i say sequence by accident (as i have been doing), i mean series.

Answer 7

2 is greater than 1 so it's divergent. You are awesome !!!