Le 2015-07-27 05:19, scott a écrit :
> Maybe I'm a bit late to the party here, probably because I'm an Engineer
> rather than a Mathematician, but this seemed a pretty crazy "proof" of
> what you get if you sum all the natural numbers up:
>
>   s= 1+2+3+4+5+6+...
>
> 4s= 4+8+12+16+...
>
> (s-4s) = 1+2+3+4+5+ 6+...
>            -4  -8  -12-...
> -3s    = 1-2+3-4+5-6+...
             ^
TYPO +2.  Not -2.
Likewise for +6, +10, +14...


So:

-3s = 1+2+3+(4-4)+5+6+7+(8-8)+9+10+11+...
-3s = 1+2+3+(0)+5+6+7+(0)+9+10+11+...

> -3s-3s = 1-2+3-4+5-6+...
>            +1-2+3-4+5-6+...
> -6s    = 1-1+1-1+1-1+1-...

No.

-6s = 2+4+6+10+12+14+18+20+22...

Then the rest is wrong.

>
> 1-(-6s)= 1-(1-1+1-1+1-1+1-...)
>         = 1-1+1-1+1-1+1-...
>         = -6s
> 1+6s   = -6s
> 12s    = -1
>
>     s   = -1/12
>
> Crazy huh?
>
> https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF


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