令s1=x-1-x(x-1)+x(x-1)^2-x(x-1)^3+……-x(x-1)^2011+x(x-1)^2012(1)两边乘(x-1)得
（x-1)s1=(x-1)^2-x(x-1)^2+x(x-1)^3-……+x(x-1)^2011-x(x-1)^2012+x(x-1)^2013(2)
(1)+(2)得
s1+(x-1)s1=x-1-x(x-1)+(x-1)^2+x(x-1)^2013
xs1 =x-1-x^2+x+x^2-2x+1+x(x-1)^2013
xs1=x(x-1)^2013
s1=(x-1)^2013
s1=原式因式分解=（x-1)^2013