# hw1 - last term and a summation containing the remaining...

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CS 173: Discrete Structures, Fall 2011 Homework 1 This homework contains 1 problem worth 15 points. 1. [15 points] Summations (a) (2 points) Rewrite r k =1 12 log( k +4) as a new summation with an index variable named n which runs from -3 to r - 4 . The terms in your new summation should be equal to the terms in the original summation. (b) (2 points) Rewrite the sum n i =1 i 2 n substituting k + 1 for n . (c) (2 points) Break up the sum t +1 p = - 1 ( p · e - p ) into three parts: its ﬁrst term, its
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Unformatted text preview: last term, and a summation containing the remaining terms. (d) (3 points) Find the values of the sum s ( n ) = ∑ n-1 i =2 3 i ( i-1) for values of n from 3 to 5. (e) (2 points) Find a closed form for ∑ n k =1 k 3 . Hint: look it up in a table of closed forms for summations. (f) (4 points) Using your result from part (e), ﬁnd closed forms for ∑ n k =1 k 3 ( n-1) and ∑ n k =2 ( n + k 3 ) . 1...
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