求幂函数(如下图)的和函数.
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求幂函数(如下图)的和函数.
![](http://img.wesiedu.com/upload/3/1a/31a3fb8e18cd2d2c41bceb5936baa0c4.jpg)
![](http://img.wesiedu.com/upload/3/1a/31a3fb8e18cd2d2c41bceb5936baa0c4.jpg)
![求幂函数(如下图)的和函数.](/uploads/image/z/19311111-63-1.jpg?t=%E6%B1%82%E5%B9%82%E5%87%BD%E6%95%B0%EF%BC%88%E5%A6%82%E4%B8%8B%E5%9B%BE%EF%BC%89%E7%9A%84%E5%92%8C%E5%87%BD%E6%95%B0.)
首先收敛域是(-1,1)
∑(n+1)²x^n
=[∑(n+1)x^(n+1)]'
=[x∑(n+1)x^n]'
=[x[∑x^(n+1)]']'
=[x[x/(1-x)]']'
=[x/(1-x)²]'
=(1-3x)/(1-x)³
∑(n+1)²x^n
=[∑(n+1)x^(n+1)]'
=[x∑(n+1)x^n]'
=[x[∑x^(n+1)]']'
=[x[x/(1-x)]']'
=[x/(1-x)²]'
=(1-3x)/(1-x)³