Sn=1+2x+3x^2…+nx^(n-1) ①当x=1 Sn=1+2+3+……+n=（n+1）n/2当x≠1 xSn=x+2x^2+…+nx^n ②①-②:(1-x)Sn=1+x+x^2+x^(n-1)-nx^n =(1-x^n)/(1-x) -nx^n∴Sn=(1-x^n)/(1-x)^2 -nx^n/(1-x)
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