Use Newton's Binomial Theorem to prove that for every integer n 2, n k=0 () -...

 

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Use Newton's Binomial Theorem to prove that for every integer n 2, n k=0 () - k (n 1)" = n". (1) In the rest of this exercise, you will give a combinatorial proof of this identity. Consider the set S = {1,2,...,n}. We have seen in class that the number of functions f: SS is equal to n". Consider a fixed integer k with 0 < k Use Newton's Binomial Theorem to prove that for every integer n 2, n k=0 () - k (n 1)" = n". (1) In the rest of this exercise, you will give a combinatorial proof of this identity. Consider the set S = {1,2,...,n}. We have seen in class that the number of functions f: SS is equal to n". Consider a fixed integer k with 0 < k