求问一个幂级数展开的问题要证Sum((a_n x^n)/(1-x)) = Sum(a_0 + a_1 + ...+ a_n) x^n就下图的题我的证明是:(a_n)/(1-x) = Sum(a_n x^n) 再带进去变成 Sum(Sum(a_n x^n) x^n) => Sum(a_0 + a_1 + ...+ a_n) x^2n结果算出来跟
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/21 18:26:52
![求问一个幂级数展开的问题要证Sum((a_n x^n)/(1-x)) = Sum(a_0 + a_1 + ...+ a_n) x^n就下图的题我的证明是:(a_n)/(1-x) = Sum(a_n x^n) 再带进去变成 Sum(Sum(a_n x^n) x^n) => Sum(a_0 + a_1 + ...+ a_n) x^2n结果算出来跟](/uploads/image/z/11535682-58-2.jpg?t=%E6%B1%82%E9%97%AE%E4%B8%80%E4%B8%AA%E5%B9%82%E7%BA%A7%E6%95%B0%E5%B1%95%E5%BC%80%E7%9A%84%E9%97%AE%E9%A2%98%E8%A6%81%E8%AF%81Sum%28%28a_n+x%5En%29%2F%281-x%29%29+%3D+Sum%28a_0+%2B+a_1+%2B+...%2B+a_n%29+x%5En%E5%B0%B1%E4%B8%8B%E5%9B%BE%E7%9A%84%E9%A2%98%E6%88%91%E7%9A%84%E8%AF%81%E6%98%8E%E6%98%AF%EF%BC%9A%28a_n%29%2F%281-x%29+%3D+Sum%28a_n+x%5En%29+%E5%86%8D%E5%B8%A6%E8%BF%9B%E5%8E%BB%E5%8F%98%E6%88%90+Sum%28Sum%28a_n+x%5En%29+x%5En%29+%3D%26gt%3B+Sum%28a_0+%2B+a_1+%2B+...%2B+a_n%29+x%5E2n%E7%BB%93%E6%9E%9C%E7%AE%97%E5%87%BA%E6%9D%A5%E8%B7%9F)
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来源:学生作业帮助网 编辑:作业帮 时间:2024/07/21 18:26:52