求数列x,3x^2,5x^3,7x^4-----前几项的和
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求数列x,3x^2,5x^3,7x^4-----前几项的和
求数列x,3x^2,5x^3,7x^4-----前几项的和
求数列x,3x^2,5x^3,7x^4-----前几项的和
解:Sn=a1+a2+a3+...+an=x+3x^2+5x^3+7x^4+...+(2n-1)x^n (1)
∴xSn=x^2+3x^3++x^4+...+(2n-1)x^(n+1) (2)
∴(1)-(2)得:
(1-x)Sn=x-2[x^2+x^3+x^4+...+x^n]-(2n-1)x^(n+1)
=x-2x^2[1-x^(n-1)]/(1-x)-(2n-1)x^(n+1)
∴Sn=x/(1-x)-2x^2[1-x^(n-1)]/[(1-x)^2]-[(2n-1)x^(n+1)]/(1-x)
求数列x,3x^2,5x^3,7x^4-----前几项的和
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