taylor expansion of $f(z)=\frac{z-1}{z+1}$

Question

Also indicate radius of convergence. In this numerical the point is not given about which we have to calculate taylor's series. So i don't know how to start.

Answer 1

Hint: First you need to specify which point you are using for the expansion. I assume you mean $z_0=0$.

Notice:

$$f(z)=\frac{z+1-2}{z+1}=1-\frac{2}{1+z}$$

The last fraction is easy to expand for $z_0=0$ using the infinite geometric series.