Prove that, for all integers n ≥ 0 and 0 ≤ k ≤n, we have (x+¹)=()+(*+¹) ++ (1) n+ k+1 k Hint: the left hand side is the number of k + 1-element subsets of {1,..., n+1}. Show that the right hand side is also equal to this number by grouping these subsets according to their largest element.

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