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# hw4 - MATH 145 HOMEWORK 4 ANDREW BERGET This is due Friday...

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MATH 145: HOMEWORK 4 ANDREW BERGET This is due Friday February 5! Problem A. When I write “Determine the generating function”, I mean write the generating function in a closed, simple form. (1) [Determine the generating function of the constant sequence a n = 1.] (2) [Determine the generating function of the nearly constant sequence a n = 5 if n 3000 and a n = 0 if 0 n < 3000.] (3) [Determine the generating function of the sequence a n which is 0 unless 3 n 20, in which case a n = 4.] (4) (2 points) Determine the generating function for the sequence a n , which is number of subsets of a set of size n . (5) (2 points) Determine the generating function for the number a k of subsets of [ n ] with k elements. (6) (2 points) Determine the generating function for the sequence a n determined by the condition that a n is zero if n is odd and is 3 n if n is even. (7) (2 points)Determine the generating function for the sequence a n determined by the condition that a n is zero if n is even and is 2 n if n is odd.
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