求和:Sn=x+2x2+3x3+…+nxn(x不等于-1)
求和:Sn=x+2x2+3x3+…+nxn(x不等于-1)
求和:Sn=x+2x2+3x3+…+nxn(x不等于-1) Sn=x+2x^2+3x^3+…………+(n-1)x^(n-1)+nx^n…………………(1) 那么: x*Sn=x^2+2x^3+3x^4+……………………+(n-1)x^n+n*x^(n+1)……(2) (1)-(2)得到: (1-x)Sn=x+x^2+x^3+……+x^n-n*x^(n+1) ===> (1-x)Sn=[x+x^2+x^3+……+x^n]-n*x^(n+1) ===> (1-x)Sn=[x*(1-x^n)/(1-x)]-n*x^(n+1) ===> Sn=[x*(1-x^n)]/(1-x)^2-[n*x^(n+1)/(1-x)].
答:Sn=1+2x+3x^2+4x^3+……+nx^(n-1) (1)x=0时,Sn=1(*) (2)x=1时,Sn=1+2+……+n=n(n+1)/2 (**) ...详情>>
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