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hw3 - CMPS 101 Summer 2009 Homework Assignment 3 1(1 Point...

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1 CMPS 101 Summer 2009 Homework Assignment 3 1. (1 Point) The last exercise in the handout entitled Some Common Functions . Use Stirling's formula to prove that Θ = n n n n 4 2 . 2. (2 Points) (Exercise 1 from the induction handout) Prove that for all 1 n : 2 1 3 2 ) 1 ( + = = n n i n i . Do this twice: a. (1 Point) using form I Ia of the induction step. b. (1 Point) using form IIb of the induction step. 3. (1 Point) Exercise 2 from the induction handout) Define ) ( n S for + Z n by the recurrence: ( ) + = = 2 if 1 2 / 1 if 0 ) ( n n S n n S Prove that ) lg( ) ( n n S for all 1 n , and hence ) (lg ) ( n n S Ω = . 4. (2 Points) a. (1 Point) Let ) ( n f be a positive, increasing function that satisfies
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