Question

Find Talor’s expansion of $f(z)=\frac{1}{(z+1)^2}$ about the point of z=-i.

Answer 1

By integrating the above Maclaurin series, we find the Maclaurin series for log(1 − x), where log denotes the natural logarithm:

{\displaystyle -x-{\tfrac {1}{2}}x^{2}-{\tfrac {1}{3}}x^{3}-{\tfrac {1}{4}}x^{4}-\cdots } {\displaystyle -x-{\tfrac {1}{2}}x^{2}-{\tfrac {1}{3}}x^{3}-{\tfrac {1}{4}}x^{4}-\cdots }