{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows page 1. Sign up to view the full content.

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
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern