Let n and k be positive integers. 1.For each j between 1 and n, find a...

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Let n and k be positive integers. 1.For each j between 1 and n, find a formula for the number of subsets of S = {1,2,, n} of size k+1 which have j as their largest element. 2. Use you formula from #1 to give a combinatorial proof of the formula n n (1) + (* + ¹) + · + (^ ^ ^²) = (x + 1) k k k ++ Let n and k be positive integers. 1.For each j between 1 and n, find a formula for the number of subsets of S = {1,2,, n} of size k+1 which have j as their largest element. 2. Use you formula from #1 to give a combinatorial proof of the formula n n (1) + (* + ¹) + · + (^ ^ ^²) = (x + 1) k k k ++

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