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

Question

anonymous · Answer

What is the common ratio of this geometric sequence?

anonymous · Answer

(1/8)? I don't know

anonymous · Answer

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?

anonymous · Answer

-2

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

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