1+x+\dots +x^{2n}=\frac{1-x^{2n+1}}{1-x}=\frac{x^{2n+1}-1}{x-1} \cr 1+(-x)+\dots +(-x)^{2n}= \frac{1-(-x)^{2n+1}}{1-(-x)}=\frac{1+x^{2n+1}}{1+x}