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Unformatted text preview: a n = a n-1 + 2 a n-2 + 3 a n-3 + 4 a n-4 ]. By constructive Induction ﬁnd Natural numbers A,B such that ( ∀ n )[ a n ≤ A · B n ]. Make B as small as possible. Given that value of B , make A as small as possible. 4. (25 points). On the planet Gork the only currency they have is a 5-cent coin and a 6-cent coin. (a) Show that 19 cents cannot be formed using Gork Currency. (b) Show that, for all n ≥ 20, n cents can be formed using Gork Currency. 5. (25 points) Let S be the statement: If T is a full binary tree then the number of leaves is one more than the number of internal nodes. (a) Prove S by WEAK induction. (You MUST do the proof by REMOVING leaves from the tree, as done in class.) (b) Prove S by STRONG induction (as done in class). 1...
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This note was uploaded on 12/04/2011 for the course CMSC 250 taught by Professor Staff during the Spring '08 term at Maryland.
- Spring '08