幂级数的和函数求下面幂级数的和函数:∑(∞ n=1) (2n-1)x^(2n-2)/2^n∑(∞ n=1) x^(2n-1)/2^n= x/(1-x^2/2)这步怎么得到的?
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![幂级数的和函数求下面幂级数的和函数:∑(∞ n=1) (2n-1)x^(2n-2)/2^n∑(∞ n=1) x^(2n-1)/2^n= x/(1-x^2/2)这步怎么得到的?](/uploads/image/z/679809-57-9.jpg?t=%E5%B9%82%E7%BA%A7%E6%95%B0%E7%9A%84%E5%92%8C%E5%87%BD%E6%95%B0%E6%B1%82%E4%B8%8B%E9%9D%A2%E5%B9%82%E7%BA%A7%E6%95%B0%E7%9A%84%E5%92%8C%E5%87%BD%E6%95%B0%EF%BC%9A%E2%88%91%EF%BC%88%E2%88%9E+n%3D1%EF%BC%89+%282n-1%29x%5E%282n-2%29%2F2%5En%E2%88%91%EF%BC%88%E2%88%9E+n%3D1%EF%BC%89+x%5E%282n-1%29%2F2%5En%3D+x%2F%281-x%5E2%2F2%29%E8%BF%99%E6%AD%A5%E6%80%8E%E4%B9%88%E5%BE%97%E5%88%B0%E7%9A%84%EF%BC%9F)
幂级数的和函数求下面幂级数的和函数:∑(∞ n=1) (2n-1)x^(2n-2)/2^n∑(∞ n=1) x^(2n-1)/2^n= x/(1-x^2/2)这步怎么得到的?
幂级数的和函数
求下面幂级数的和函数:
∑(∞ n=1) (2n-1)x^(2n-2)/2^n
∑(∞ n=1) x^(2n-1)/2^n= x/(1-x^2/2)
这步怎么得到的?
幂级数的和函数求下面幂级数的和函数:∑(∞ n=1) (2n-1)x^(2n-2)/2^n∑(∞ n=1) x^(2n-1)/2^n= x/(1-x^2/2)这步怎么得到的?
∑(∞ n=1) x^(2n-1)/2^n= x/(1-x^2/2)
对x两边求导
∑(∞ n=1) (2n-1)x^(2n-2)/2^n= 求导x/(1-x^2/2)