Use the binomial theorem to prove the following equalities for any natural number n ∈ n. it is enough in each case to specify x and y in the binomial theorem and show that this results in the given equality. (i’ve written the left-hand sides in two ways–in summation notation and written out in full.) (a) (hammack §3.4 #5 ) xn k=0 n k = n 0 + n 1 + · · · + n n = 2n (b) (hammack §3.4 #7 ) xn k=0 3 k n k = n 0 + 3 n 1 + 32 n 2 + · · · + 3n n n