1. ## Taylor series

hi
i need help with finding Taylor series for f(z)=1/(4-5z) at z=i

thx

2. Originally Posted by dft
hi
i need help with finding Taylor series for f(z)=1/(4-5z) at z=i

thx
The simplest way to do that is to set z= u+ i so that u= z- i. Then the f(u)= 1/(4- 5(u+ i))= 1/(4- 5i- 5u) or, dividing numerator and denominator by 4- 5i, this is $\frac{\frac{1}{4-5i}}{1- \frac{5}{4-5i}u}$ and recall that $\frac{a}{1- r}$ is the sum of the geometric series $\sum_{n=0}^\infty ar^n$.

3. thanks