Unformatted text preview: n 3 + 2 n whenever n is a nonnegative integer. Proof by induction: Base step: n = 1. Then n 3 + 2 n = 3, so 3  n 3 + 2 n . Induction step: we assume 3  n 3 +2 n , and we need to show 3  ( n +1) 3 +2( n +1). Now, ( n + 1) 3 + 2( n + 1) = n 3 + 3 n 2 + 3 n + 1 + 2 n + 2. We can arrange this as n 3 + 2 n + 3 n 2 + 3 n + 3. By the inductive hypothesis, 3  n 3 + 2 n . Obviously 3  3 n 2 + 3 n + 3, so 3  ( n + 1) 3 + 2( n + 1). 1...
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 Fall '08
 Miller
 Math, Mathematical Induction, Inductive Reasoning, Natural number, Peano axioms, geometric sums

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