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CSC 236                     Homework Exercise 1                 Winter 2008
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Due: by 10am on Thu 17 Jan
Worth: 1.5%

For each question, please write your answer formally following the detailed
format given in lecture (in particular, define P(n) carefully).  Keep in
mind that approximately half of the marks for each question will be given
purely for having the correct proof structure, written up clearly and
precisely, irrespective of the correctness of the proof.

1.  What is the value of \sum_{i = 0,1,...,n} 2^{i+1} for each n (- N?
    Make a conjecture and prove it formally.

2.  What amounts of postage is it possible to make using only 3c and 8c
    stamps?  Make a conjecture and prove it formally.
    (NOTE:  Give only *one* proof, using any one of the methods outlined in
    the lecture notes -- the goal here is to make sure you understand how
    to prove this type of question, *not* to have you blindly "plug in"
    numbers into some other proof with no understanding of its structure or
    how it works...)