Sn=2+5x+8x²+11x的三次方+.+(3n-1)x的n-次方,求和

Sn=2+5x+8x²+11x的三次方+.+(3n-1)x的n-次方,求和
Sn=2+5x+8x²+11x的三次方+.+(3n-1)x的n-次方,求和

Sn=2+5x+8x²+11x的三次方+.+(3n-1)x的n-次方,求和
Sn=2+5x+8x²+11x的三次方+.+(3n-1)x的n-1次方,
x*Sn=2x+5x²+8x^3+11x^4+.+(3n-1)x^n,
相减得
(1-x)Sn=2+3(x+x^2+.+x^n-1)-(3n-1)x^n,
=2+3x*(1-x^(n-1))/(1-x)-(3n-1)x^n,
Sn=[(3n-1)x^(n+1)-(3n+2)x^n+x+2]/(1-x)^2

Sn=[(3n-1)x^(n+1)-(3n+2)x^n+x+2]/(1-x)^2