5. (8 points) Which of the following statements must be true? Which must be false? If the statement is false, explain why or give an example demonstrating that it is false. If the statement is true, you should provide a short explanation or prove that it is true. (a) 100 z (EY = 2 k=1 3 1 g 00 (b) If the power series 2 akin,\" converges for m = 2 and diverges for a: = 5, then it must converge Ic=1 for at = 1. 00 (c) If lim ak = 0, then 2 ak must converge. k>oo k=1 272,2 + 10 00 ((1) Let 3\" = a1 + a2 + a3 + - - - + an be the nth partial sum of the series 2 wk. If sn = n2 + 2 k=1 1 00 then the series 2 wk must diverge. 16:1