225_01_intro - Whatiswrongwithmyinductionproof?

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1 What is wrong with my induction proof? In a drunken haze I decided that the solution to the recurrence T(1)=1, T(n)= 1  + T(n-1) is  1 + 2 + 3 + … + n. Theorem: The solution to the recurrence is n(n+1)/2. Proof. [Basis] T(1)=1 and 1 *(1+1)/2 = 1 as required. [Induction step] Assume that 1 + 2 + … + n-1 + n = n(n+1)/2. We want to prove that 1 + 2 + … + n-1 + n + (n+1) = (n+1)(n+2)/2 = (n 2  +3n  +2)/2. By induction, 1 + 2 + … + n= n(n+1)/2. So 1 + 2 + . . + n + (n+1)=  n(n+1)/2 + (n+1). Simplifying: (n 2  + n + 2n + 2)/2= (n 2  +3n +2)/2 as required.
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2 CSC 225: Design and Analysis of Algorithms Dr. Wendy Myrvold, ECS 552, wendym@csc.uvic.ca Cartoon from: http://www.uoregon.edu/~ftepfer/SchlFacilities/TireSwingTable.html
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3 Announcements Assignment #1 is posted (on connex and on our class web page). Part A Written Questions: due Wed. Sept. 21 Part B Programming Questions: due Fri. Sept. 23 It’s better to hand in a partially completed assignment then to hand in nothing at all. You must pass the assignments to pass  the course. Lab 1 is posted: print the code and test it on your computer before lab Sept. 12. Please make sure you sign the attendance sheet every class to get credit for attending. Bring your schedule to class next Tuesday to help me in choosing office hours. Powerpoint slides will be posted.
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4 Class Materials and Announcements Connex will be used for posting model solutions and other private class  resources and also for sending e-mail announcements to the class. If you have   connex?  next to your name on the class signature list, this  means I did not see your name on Tuesday on the class roster.  Instructions for getting connex access are at the bottom of our class web  page.
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5 To learn more about the Co-operative Education Program and and Career Services on campus, visit: http://www.uvic.ca/coopandcareer OR see/email: Duncan Hogg ( dshogg@uvic.ca ), ECS 230 Application form available outside the ECSM Co- op Office (ECS 204).
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225_01_intro - Whatiswrongwithmyinductionproof?

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