Using the binomial coefficients (2) = n n! (n-k)!k! (1) The sum first n integers: 1 + 2 + ... + n = prove that the following is correct: = 2n k=0 Use part 1 to argue that given a set A = {a₁,..., an} with n objects, that the number of subsets of A, that is the number of sets in P(A), is 2". You may find the following helpful, but I do not guarantee that you will need all of these. The sum of a geometric series 1 + r + r² + ... + pn = n(n+1) 2 The sum of first n squared integers: 1² + 2² + ... pn+1-1 r-1 ·+n². n(n+1)(2n+1)

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A: We can answer the question as below.

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