Determine whether the following statements are true and give an explanation or counterexample.

a. Let p_n be the nth-order Taylor polynomial for f centered at 2. The approximation p₃(2.1) ≈ f(2.1) is likely to be more accurate than the approximation p₂(2.2) ≈ f(2.2).

b. If the Taylor series for f centered at 3 has a radius of convergence of 6, then the interval of convergence is [-3, 9].

c. The interval of convergence of the power series ∑c_k x^k could be [-7/3 , 73].

d. The Maclaurin series for f(x) = (1 + x)¹² has a finite number of nonzero terms.