A weird infinity problem. [duplicate]

A weird infinity problem. I saw this on youtube but could not understand it:
Let us add 1 + 2 + 4 + 8 + 16 + ... up to infinity
x=(1+2+4+8+...)
= 1(1+2+4+8+...) = (2-1)(1+2+4+8+...) = (2+4+8+16+...)-(1+2+4+8+...) = -1
x=-1

Now that is weird since we are adding up to infinity towards the positive side yet we end up with a negative number. Somebody please explain me why.

• As long as only sums are involved, everything is fine. But to substract $+\infty$ from $+\infty$ (which you do as soon as a minus sign appears) can lead to chaos. This has been explained several times on the site. – Did Oct 30 '13 at 12:09
• can u provide me a link? – Shaurya Gupta Oct 30 '13 at 12:18
• – Gerry Myerson Oct 30 '13 at 12:34