解一道初一试题,(1+x)(1-x)=1-x2(1-x)(1+x+x2)=1-x3(1-X)(1+x+x2+x3)=1-x4计算2+22+23+……2n的值
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![解一道初一试题,(1+x)(1-x)=1-x2(1-x)(1+x+x2)=1-x3(1-X)(1+x+x2+x3)=1-x4计算2+22+23+……2n的值](/uploads/image/z/5935199-23-9.jpg?t=%E8%A7%A3%E4%B8%80%E9%81%93%E5%88%9D%E4%B8%80%E8%AF%95%E9%A2%98%2C%281%2Bx%29%281-x%29%3D1-x2%281-x%29%281%2Bx%2Bx2%29%3D1-x3%281-X%29%281%2Bx%2Bx2%2Bx3%29%3D1-x4%E8%AE%A1%E7%AE%972%2B22%2B23%2B%E2%80%A6%E2%80%A62n%E7%9A%84%E5%80%BC)
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解一道初一试题,(1+x)(1-x)=1-x2(1-x)(1+x+x2)=1-x3(1-X)(1+x+x2+x3)=1-x4计算2+22+23+……2n的值
解一道初一试题,
(1+x)(1-x)=1-x2
(1-x)(1+x+x2)=1-x3
(1-X)(1+x+x2+x3)=1-x4
计算2+22+23+……2n的值
解一道初一试题,(1+x)(1-x)=1-x2(1-x)(1+x+x2)=1-x3(1-X)(1+x+x2+x3)=1-x4计算2+22+23+……2n的值
(1-x)(1+x+x^2+x^3+…+x^n)=1-x^(n+1)
x=2时:
(1-2)(1+2+2^2+2^3+…+2^n)=1-2^(n+1)
化简 1+2+2^2+2^3+…+2^n=2^(n+1)-1
∴2+2^2+2^3+…+2^n= 2^(n+1)-2
学了等比数列就好算了