Euler sum of a divergent series So I have a series $1+0+(-1)+0+(-1)+0+1+0+1+0+(-1)+...$
Is it correct to rearrange this as $1+0+(-1)+0+1+0+(-1)+0+1+0+(-1)+0...$
The second problem can be done as an Euler sum and the answer is $\frac{1}{2}$. In general, I know that absolutely convergent series can be rearranged but I'm not sure what the rule is for this case

One can only rearrange absolutely convergent series (positive terms convergent as well). For semi convergent series one can prove that rearranging can lead to any limit including making the series divergent. Numerically there is a very rich field around divergent series.
