2. Suppose that f(z) = Zak(m 4)* and suppose it is known that (9) diverges but that the series represented by Z 2% ay, k=0 k=0 converges. A. [6 pts] Indicate whether the following series must converge, must diverge, or could converge or diverge by filling in the appropriate circle. No justification is necessary. (i) The series represented by f(1): Q must converge O must diverge O could converge or diverge. (ii) The series f(5): Q must converge O must diverge O could converge or diverge. oo (iii) The series represented by Zkak: O must converge O must diverge O could converge or diverge. k=0 oo B. [2 pts] State the largest possible interval of convergence for the series f(z) = Zak(m 4)* consistent with the k=0 given information. Write your answer in the box provided. 3. [6 pts] Find the third degree Taylor polynomial of f centered at x = 2 for f(z) = Vdz 7