1. Find the Taylor series expansion of the function f (z) = 1-z/1+z centered at 0, using two methods
a) By direct application of the coefficient formula. Produce three terms of the expansion
b) Without the direct application of the coefficient formulae.
c) Giving the required reasoning, find the radius of convergence.
2. Derive the Laurent series expansion of the function f (z) = 1/z2 centered at 1 and convergent on the annulus 1 < |z-1| < ∞.
3. Find the Taylor series expansion of the function f (z) = 1/(1-z)3 centered at 0. Find the radius of convergence explaining all your steps.