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Unformatted text preview: a 1 = 3, and let a n = 2 a n11 for all n ≥ 2. [1 point] (i) Give the values of a 2 , a 3 , a 4 , a 5 , and a 6 . [2 points] (ii) Guess a nonrecursive formula for a n . [2 points] (iii) Use induction to prove that your formula from (ii) is correct. 5 [5 points] Question 6. Use induction to prove that n ! > n 3 for all n ≥ 6. (Recall that n ! means 1 × 2 × 3 × ··· × n .) To save you time with computations, I include some values of n ! and n 3 . Note that there’s a very good reason I told you to start with n = 6. n 1 2 3 4 5 6 n ! 1 2 6 24 120 720 n 3 1 8 27 64 125 216 6...
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 Spring '08
 Staff
 Congruence, Natural number, congruences, Congruence relation

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