Exercise. Consider the function f(2) = . We find the radius of convergence two ways: Exercise. We can use the rules of composition to find the radius of convergence for the Taylor series centered at z = 0 for f() = Since: 1 - 4x 1 - (4x] ) we would find the Taylor series for f(x) by substituting 42 for z in the Taylor series centered at z = 0 for . This also applies for the radius of convergence: The series for _ converges when | |