Question

幂级数 求（x-2）e∧（-x）在x=1处的泰勒级数

Answer 1

为方便,令t=x-1

(x-2)e^(-x)=(t-1)e^(-t-1)

=1/e[te^(-t)-e^(-t)]

=1/e[t(1-t+t^2/2!-t^3/3!+...)-(1-t+t^2/2!-t^3/3!-..)]

=1/e[ -1+2t-t^2(1+1/2!)+t^3(1/2!+1/3!)-.-(-1)^nt^n(1/(n-1)!+1/n!)+...]