求级数∑(n^2/n!)x^n的和函数,n(1,∞)如题,实在不行给个思路也行.偶对数学实在是无能为力,

Question

求级数∑(n^2/n!)x^n的和函数,n(1,∞)
如题,实在不行给个思路也行.偶对数学实在是无能为力,

Answer 1

∑(n^2/n!)x^n=∑(n/(n-1)!)x^n=∑(1/(n-1)!+1/(n-2)!)x^n (约定1/(-1)!=0)=∑(1/(n-1)!)x^n+∑(1/(n-2)!)x^n (事实上这一步要求两个级数分别收敛,这个验证一下收敛域即可)=x∑(1/n!)x^n+x+x^2∑(1/n!)x^n+x^2而∑(1...