Question

\求和Sn=1+2x+3x^2+```+(n-1)x^(n-2)+n*x^(n-1)

Answer 1

若x=1Sn=1+2+3+……+n=n(n+1)/2若x不等于1xSn=x+2x^2+3x^3+……+n*x^n所以Sn-x*Sn=1+x+x^2+x^3+……+x^(n-1)-n*x^nSn(1-x)=1*(1-x^n)/(1-x)-nx^n=[1-x^n-nx^n+n*x^(n+1)]/(1-x)所以Sn=[1-x^n-nx^n+n*x^(n+1)]/(1-x)^...