Hi please could you assist me: questions posted below:

Assuming the function f is holomorphic in the disk , prove that is also holomorphic in D(0,1) and find its derivative?????

Find the radii of convergence of the following series stating which result is being used.

(a)

(b)

(c)

(A)

Using Ratio Test:

=

So is rad. of convergence (z-1)/2 and converging since it is less than 1??

(B)

Using Ratio Test:

Hence, is ROC infinity and diverging since it is greater than 1?

(C)

Using Ratio Test:

So is ROC 0 and converging since it is less than 1?