计算下列各题; (x-1)(x+1)=___ (x-1)(x²+x+1)=___ (x-1)(x³+

(x-1)(x+1)=x²-1, (x-1)(x²+x+1)=x³-1, (x-1)(x³+x²+x+1)=x^4-1

1),(x-1)(x^n+x^n-1+x^n-2+…+x+1)的结果是x^(n+1)-1

2),证明:
(x-1)(x^n+x^n-1+x^n-2+…+x+1)
=x(x^n+x^n-1+x^n-2+…+x+1)-(x^n+x^n-1+x^n-2+…+x+1)
=x^(n+1)+x^n+x^n-1+x^n-2+…+x-(x^n+x^n-1+x^n-2+…+x+1)
=x^(n+1)-1

证明：x^n+x^n-1+x^n-2+…+x+1，这是一个首项为1，公比为x的等比数列，共有n+1项，求和公式s=a(1-q^n)/(1-q),代入=(1-x^(n+1))/(1-x),再乘以x-1，刚好等于x^(n+1)-1