Question

How come this is true???

Each term in this infinity series is 2 times the last term:

s=1+2+4+8+16+...

factor out a 2:

s=1+2(1+2+4+8+...)

Now notice that's the original series

s=1+2s

s=-1

How come? How can this possibly exist and not be s=infinity?

Answer 1

may be because \[2*\infty-\]

Answer 2

i mean 2x(infinity)-(infinity) in not equal to (infinity) it is rather not defined

Answer 3

Hmm, I suppose so, but I've read about it and heard about it before. It seems like it has some significance somehow, but I don't understand how this could be useful at all.

Answer 4

its an infinte gp series........

Answer 5

Yeah, it's a geometric series but how does 1/(1-2)=-1 really mean anything? It's very confusing that adding a bunch of positive numbers to infinity somehow gives you -1. I just don't get it.

Answer 6

but a/(1-r) is applicable when r<1

Answer 7

sorry mod(r)<1

Answer 8

@Kainui

Answer 9

u will use a/(r-1) here

Answer 10

Hmm, sure but what about this: http://en.wikipedia.org/wiki/1_%2B_2_%2B_4_%2B_8_%2B_%E2%80%A6

Answer 11

the sum will be +1

Answer 12

cant say then....

Answer 13

positive infinite. series converging to a negative no.............impossible