观察下列各式: (x-1)(x+1)=x2-1 (x-1)(x2+x+1)=x3-1 (x-1)(x3+x2+x+1)=x4-1 … 根据前面规律可得 (x-1)(xn+1+xn+…+x+1)=_.

问题描述:

观察下列各式:
(x-1)(x+1)=x2-1                       
(x-1)(x2+x+1)=x3-1
(x-1)(x3+x2+x+1)=x4-1

根据前面规律可得 (x-1)(xn+1+xn+…+x+1)=______.

根据题意得:(x-1)(xn+1+xn+…+x+1)=xn+2-1.
故答案为:xn+2-1.