Sol_2 - CMPSC 465 SOLUTIONS TO ASSIGNMENT 2 This assignment...

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CMPSC 465 SOLUTIONS TO ASSIGNMENT 2 This assignment is worth a total of 100 points Fall 2008 1. [20 Points: solution 18 + simplify 2] 3 n +3 n - 1 8 + 3 n - 2 8 2 +3 n - 3 8 3 + . . . +8 n is a geometric progression with ratio 8 3 . Its sum is next - first ratio - 1 = 8 n +1 / 3 - 3 n 8 / 3 - 1 = 8 n +1 - 3 n +1 5 where the next term is the product last × ratio and the last fraction results from the previous fraction through multiplication of numerator and denominator by 3. 2. [20 Points: a 3 + b 3 + c 3 + d 3 + e 4 + f 4] (a) n ( n + 1) and 2000 n 2 are both quadratic polynomials and thus have the same growth rate. (b) 100 n 2 is quadratic and has thus a smaller growth rate than the cubic 0 . 01 n 3 . (c) All logarithm functions have the same growth rate. (d) log 2 ( n 2 ) = 2 log 2 n . Thus lim n →∞ (log 2 n ) 2 log 2 ( n 2 ) = lim n →∞ (log 2 n )(log 2 n ) 2 log 2 n = lim n →∞ log 2 n 2 = , which shows that (log 2 n ) 2 has a larger rate of growth than log 2 ( n 2 ) . (e)
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Sol_2 - CMPSC 465 SOLUTIONS TO ASSIGNMENT 2 This assignment...

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