这道题的知识点xe^x=(∞∑n=1)bnx^n,则系数bn=;

Question

这道题的知识点
xe^x=(∞∑n=1)bnx^n,则系数bn= ;

Answer 1

首先应该知道e^x = (∞∑n=0)x^n/n!
故xe^x = x*(∞∑n=0)x^n/n!= (∞∑n=0)x^(n+1)/n!= (∞∑n=1)x^n/(n-1)!
故 bn = 1/(n-1)!;