Mathematics, 31.07.2019 21:30 heyitzmeamelie

We counted ƒ(n), the number of subsets of {1, . . , n} with no consecutive integers. now, we will further refine this question: let ƒ(n, k) be the number of subsets of size k of {1, . . , n} with no consecutive integers.
find a formula for ƒ(n, k), then deduce an identify from the fact that ƒ(n) = ∑ₖƒ(n, k).

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We counted ƒ(n), the number of subsets of {1, . . , n} with no consecutive integers. now, we will f...