计算下列各题; (x-1)(x+1)=___ (x-1)(x²+x+1)=___ (x-1)(x³+x²+x+1)=___1)猜想(x-1)(x^n+x^n-1+x^n-2+…+x+1)的结果是___2)证明你的猜想
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![计算下列各题; (x-1)(x+1)=___ (x-1)(x²+x+1)=___ (x-1)(x³+x²+x+1)=___1)猜想(x-1)(x^n+x^n-1+x^n-2+…+x+1)的结果是___2)证明你的猜想](/uploads/image/z/1024346-2-6.jpg?t=%E8%AE%A1%E7%AE%97%E4%B8%8B%E5%88%97%E5%90%84%E9%A2%98%3B+%28x-1%29%28x%2B1%29%3D___+%28x-1%29%28x%26%23178%3B%2Bx%2B1%29%3D___+%28x-1%29%28x%26%23179%3B%2Bx%26%23178%3B%2Bx%2B1%29%3D___1%29%E7%8C%9C%E6%83%B3%28x-1%29%28x%5En%2Bx%5En-1%2Bx%5En-2%2B%E2%80%A6%2Bx%2B1%29%E7%9A%84%E7%BB%93%E6%9E%9C%E6%98%AF___2%29%E8%AF%81%E6%98%8E%E4%BD%A0%E7%9A%84%E7%8C%9C%E6%83%B3)
计算下列各题; (x-1)(x+1)=___ (x-1)(x²+x+1)=___ (x-1)(x³+x²+x+1)=___1)猜想(x-1)(x^n+x^n-1+x^n-2+…+x+1)的结果是___2)证明你的猜想
计算下列各题; (x-1)(x+1)=___ (x-1)(x²+x+1)=___ (x-1)(x³+x²+x+1)=___
1)猜想(x-1)(x^n+x^n-1+x^n-2+…+x+1)的结果是___
2)证明你的猜想
计算下列各题; (x-1)(x+1)=___ (x-1)(x²+x+1)=___ (x-1)(x³+x²+x+1)=___1)猜想(x-1)(x^n+x^n-1+x^n-2+…+x+1)的结果是___2)证明你的猜想
(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