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Unformatted text preview: CS 173: Discrete Structures, Fall 2010 Homework 1 Solutions This homework contains two problems worth a total of 20 points, plus an on-line survey to complete. It is due on Friday, September 3rd at 4pm. The homework dropboxes are towards the east end of the main corridor of the Siebel basement, between the lounge area and the vending machines. Put your homework in the box marked with your discussion section. Be sure that your name and the day/time of your discussion section (e.g. “Monday 12”) are easy to read at the top of your homework. 1. [5 points] Demographic survey Fill out the online demographic survey at https://illinois.edu/sb/sec/142974 Your individual answers (which will be kept confidential) will help us advise you better this term. Summaries of responses from the class as a whole will improve the CS department’s on-going curriculum development efforts. 2. [12 points] Summations (a) (2 points) Rewrite ∑ p +1 k =0 log 2 k as a sum whose terms are identical but in which the index variable is named m and m runs from 5 to p + 6 . [Solution] Notice that the limits of the desired summation are five greater than the limits of the original summation, so m = k + 5 . Therefore, k = m − 5 . Thus, we obtain p +6 summationdisplay m =5 log 2 ( m − 5) . Note: It has been pointed out that the first term of the given sum is undefined (for the purposes of this course). No finite power of 2 will ever give you 0, although you can get really close. However, nothing stops us from rewriting the summation formally as we have done above. If you are still really bothered by the mention of undefined terms, you can rest assured that it is in fact possi-...
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