Question

f(x)=xe^-2x展开成x的幂级数怎么做

Answer 1

• 这个的思修其实很简单，就是以e^x为基础然后逐个换
• 令2x换成x
• 然后每项乘以x

Answer 2

e^x= 1+x/1!+x^2/2!+....
e^(-2x) = 1 - (2/1!)x + (4/2!)x^2+...+ (-1)^n . (2^n/n!)x^n+...
f(x) =x.e^(-2x)
= x - (2/1!)x^2 + (4/2!)x^3+...+ (-1)^n . (2^n/n!)x^(n+1)+...