Sn=2+5x+8x²+11x的三次方+.+(3n-1)x的n-次方,求和
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![Sn=2+5x+8x²+11x的三次方+.+(3n-1)x的n-次方,求和](/uploads/image/z/978294-30-4.jpg?t=Sn%3D2%2B5x%2B8x%26%23178%3B%2B11x%E7%9A%84%E4%B8%89%E6%AC%A1%E6%96%B9%2B.%2B%283n-1%29x%E7%9A%84n-%E6%AC%A1%E6%96%B9%2C%E6%B1%82%E5%92%8C)
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