Prove the following statements using induction. k=1 (a) For all n N, we have 1 = (k=1 k) . (b) Let n E N, then Vn > 7, we have n! > 3. (c) Define the {unn20 by the rule uo ne Z with n 0 we have 1 < Un < 2. (Hint: try computing u, U2, U3 to better understand the sequence.) = 2 and Un+1 = 2 un for n > 0. Then for every 1 Un