Quiz5_sol - f 2 k-1 = f 2 k show f 1 ·· f 2 k-1 f 2 k 1...

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Solutions to Quiz 5 Question 1 Base case: n = 5 , 2 5 = 32 > 5 2 = 25 Inductive step: Assume 2 k > k 2 , show 2 k +1 > ( k + 1) 2 = k 2 + 2 k + 1 . 2 k +1 = 2 · 2 k > 2 k 2 > k 2 + 2 k + 1 = ( k + 1) 2 , which is true k > 2 . Question 2 Base case: n = 1 , f 1 = 1 = f 2 . Inductive step: Assume f 1 + · · ·
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Unformatted text preview: + f 2 k-1 = f 2 k , show f 1 + ··· + f 2 k-1 + f 2 k +1 = f 2 k +2 . LHS = f 1 + ··· + f 2 k-1 + f 2 k +1 = f 2 k + f 2 k +1 = f 2 k +2 = RHS. 1...
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