若1+x+x²+x³=0 (显然x≠1)
(1-x)(1+x+x²+x³)=1-x^4=0
x^4=1
即x²=1
所以
1+x+x²+x³+.+x²ºº¹
=(1-x)(1+x+x²+x³+.+x²ºº¹)÷(1-x)
=(1-x^2002)÷(1-x)
=[1-(x²)^1001]÷(1-x)
=[1-1的1001次方]÷(1-x)
=[1-1]÷(1-x)
=0