Please help me with these question. SHow all you work. Thank you 1. Prove that VKE N, 1k+ 2k + · · · + nk € ©(nk+1). 2. Suppose that the functions f1, f2, g1, g2 : N → R≥0 are such that f1 = O(g1) and f2 = ☹(g2). Prove that (f1+f2) = O(max{g1, g2}). Here (f1 + f2)(n) = f1(n) + f2(n) and max{g1, g2}(n) = max{g1(n), g2(n)}