Discrete and Foundational Mathematics I quiz 7 Solutions

3 induction step prove 1 is true for n k 1 so we must

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Unformatted text preview: ssume 13 + 23 + 33 + · · · + k 3 = k (k + 1) 2 2 . 3. Induction Step. Prove (1) is true for n = k + 1. So we must prove (k + 1) (k + 2) 2 3 13 + 23 + 33 + · · · + k 3 + (k + 1) = So LHS = = 13 + 23 + 33 + · · · + k 3 + (k + 1)3 k (k + 1) 2 = (k + 1)2 2 = (k + 1) 2 = (k + 1) 2 3 + (k + 1) k 2 2 + (k + 1) k2 +k+1 4 k 2 + 4k + 4 4 2 2 = (k + 1) (k + 2) 4 (k + 1) (k + 2) 2 = RHS. = QED 2 2 . 2) Woman in front of a line of n people. Man in back of this line. Prove that somewhere in the line t...
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This note was uploaded on 01/31/2014 for the course MATH 187 taught by Professor Holmes during the Fall '08 term at Boise State.

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