hw08 sol - Spring-2011 CMSC 250: Homework 8 Due: Wed Apr 6,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Spring-2011 CMSC 250: Homework 8 Due: Wed Apr 6, 2011 NOTE: Due AT THE BEGINNING of Recitation! COURSE WEBSITE: http://www.cs.umd.edu/ gasarch/250/S11.html (NOTE- there is a Tilda before gasarch. It may be easier to get to the course website via the dept webpage (go to class webpages) or gasarchs homepage (it will be obvious).) 1. (0 points) What is your name? Write it clearly. Staple your HW. What is your SECTION NUMBER. WHERE and WHEN are you taking the SECOND MIDTERM. (SEE shortsyll to see WHERE.) If you cannot make the midterm time and have NOT been in contact with Dr. Gasarch about it then contact him ASAP (gasarch@cs.umd.edu). 2. (25 points) Define a n as follows: a 1 = 1, a 2 = 21, and ( n 3)[ a n = a 2 n- 1 + a 3 d n/ 2 e + 3]. Show that, for all n 1, a n 1 (mod 4). SOLUTION TO QUESTION 2 BASE CASE: a 1 = 1 1 (mod 4). a 2 = 21 1 (mod 4). INDUCTION HYPOTHESIS: For all 1 m < n a m 1 (mod 4). In particular a n- 1 1 (mod 4) and a d n/ 2 e 1 (mod 4). INDUCTION STEP: a n = a 2 n- 1 + a 3 d n/ 2 e + 3 1 2 + 1 3 + 3 5 1. 3. (25 points) Define a n as follows: a 1 = 1, a 2 = 10, a 3 = 500, a 4 = 1000 and ( n 5)[ a n = a n- 1 + 2 a n- 2 + 3 a n- 3 + 4 a n- 4 ]....
View Full Document

Page1 / 4

hw08 sol - Spring-2011 CMSC 250: Homework 8 Due: Wed Apr 6,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online