There is a Wikipedia page for that serie which uses analytic continuation to obtain -1/2.

S1=1+1+1+1+... S2= 1-1+1-1+... S1+S2= 1+2+0+2+0+... Only sum is shifted like what is done for other series summation.

And finally for more fun: S1=-1/2 S1/6=-1/12 So: 1/6+1/6+1/6+1/6+... = 1+2+3+4+...

## Re: 1+1+1+1+...=-1/2

There is a Wikipedia page for that serie which uses analytic continuation to obtain -1/2.

S1=1+1+1+1+...

S2= 1-1+1-1+...

S1+S2= 1+2+0+2+0+...

Only sum is shifted like what is done for other series summation.

And finally for more fun:

S1=-1/2

S1/6=-1/12

So:

1/6+1/6+1/6+1/6+... = 1+2+3+4+...