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EX_2-6.pdf - Homework 2 1 2n is O(n Base Case C =2 k =0 n >...

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Homework 2 1. 2 n is O(n!) Base Case: C =2 k =0 n > k, 2 n Æ C ( n )! 1 > 0 , 2 1 Æ 2(1)! 2 Æ 2 X Induction Hypothesis: 2 K is O ( K !) 2 K < C ( K !) 2 K < 2( K !) for all K > k Induction Steps: want to prove: 2 K +1 is O(K+1)! ( this is the same as 2 K +1 < 2(K+1)! ) 2 K (2) < 2( K !)(2) Æ 2(
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