Question

Ok, time for me to quit for the night, but I'll leave y'all with this to scratch your heads about:

Infinite sum of 1+2+4+8+16+32+ . . . = -1.

Proof:
Multiply series by 1 (which should not change the sum); however, I'm going to express 1 as (2-1).
2-1=1.
(2-1)(1+2+4+8+16+...)
=(2+4+8+16+32+...)+(-1-2-4-8-16-...)
All the opposites cancel out and all that is left is -1.

Pretty screwy, huh?

Answer 1

doesnt work like this

answer is still infinity

Answer 2

in a nutshell
you subtracting an n+1 term summation from an n term summation
since both summations are to infinity so they must have the same amount of terms

thus
n+1=n
1=0

Answer 3

ive asked my professor this before
sorry i dont remember the full explanation

Answer 4

The explanation I give most people is "infinity is weird." ;-)

Answer 5

Of course it's a bogus proof, but it's fun to show people to give them that paradox feeling.

Answer 6

i will represent the infinite summation as x

x= infinity

2x and 1x
2x-1x=x(2-1)=x(1)

its not nice to trick people

Answer 7

LOL, what do you mean "it's not nice to trick people."
It's a puzzle, the object is to find out what's wrong with it. You obviously weren't tricked.

Answer 8

misleadddd*

Answer 9

Please.
Would you have felt better if I prefaced it with the statement, "The following is a bogus proof, try to find what's wrong with it."?
I'm sure it's pretty clear to anyone that it's not serious.

Answer 10

Buncha grouches 'round here . . .