## Disco619 one year ago Am I right about the answer you get when you add up to Infinity? Math Experts Only, Anyone else is Welcome too.

1. Disco619

$1+2+4+8+16... = \infty$ Fact $1 \times x = x$ Fact $(1)(1+2+4+8+16...) = 1+2+4+8+16...$ Fact $2-1 = 1$ Fact $(2-1)(1+2+4+8+16...) = 1+2+4+8+16...$ ALSO $(2-1)(1+2+4+8+16...) = 2+4+8+32...-1-2-4-8-16-32...$ Almost everything on the right side cancels out, guess what's left behind? $= -1$ $1+2+4+8+16... = -1$ $\infty = -1$ How about that?

2. Disco619

Correction: $(2-1)(1+2+4+8+16...) = 2+4+8+16+32...-1-2-4-8-16-32...$ |dw:1433714372127:dw|

3. anonymous

I may be wrong, but your sum would be equivalent to $\sum_{n=0}^{\infty}2^{n}$ A rearrangement of a series would only converge to the same value if it were absolutely convergent, but this series is divergent. Thus I'm sure you could do a manipulation and get any result you want.

4. Disco619

Fair enough, but this side of Maths is still interesting though, it isn't so 'Perfect'? If that's how someone would put it.

5. anonymous

Of course, a lot of this stuff is fascinating in my eyes. It's what makes it so fun to study :)

6. Disco619

I'll just leave this Question open for a bit and Bump it for others to see. Thanks!

7. ybarrap

If the series is not absolutely convergent then the addition of infinite sums is not commutative. You might want to take a look at https://en.wikipedia.org/wiki/Alternating_series#Rearrangements Here we are talking about creating a convergent series from a divergent one. Since the original series is not absolutely convergent, then commutation is not allowed.