Question

将函数y=1÷（x∧2+3x+2）展开成x+4的幂级数

Answer 1

y=1/(x²+3x+2)

=1/(x+1)(x+2)

=1/(x+1)-1/(x+2)

=1/(x+4-3)-1/(x+4-2)

记t=x+4,只需将其化为t的幂级数即可.

y=1/(t-3)-1/(t-2)

=-1/3*1/(1-t/3)+1/2*1/(1-t/2)

=-1/3*[1+t/3+t²/3²+...]+1/2*[1+t/2+t²/2²+...]