Data Str &amp; Algorithm HW Solutions 88

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14 Analysis Techniques 14.1 Guess that the solution is of the form an 3 + bn 2 + cn + d. Since when n =0 the summation is 0, we know that d =0 .W eh a v eth e following simultaneous equations available: a + b + c =1 8 a +4 b +2 c =5 27 a +9 b +3 c =1 4 Solving this set, we get a =1 / 3 , b =1 / 2 and c =1 / 6 , yielding Equa- tion 2.2. 14.2 Guess that the solution is of the form an 4 + bn 3 + cn 2 + dn + e. Since when
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Unformatted text preview: following simultaneous equations available: a + b + c + d = 1 16 a + 8 b + 4 c + 2 d = 9 81 a + 27 b + 9 c + 3 d = 36 256 a + 64 b + 16 c + 4 d = 100 Solving this set, we get a = 1 / 4 , b = 1 / 2 , c = 1 / 4 , and d = 0 . Thus, the closed form formula is n 4 + 2 n 3 + n 2 4 . The student should verify by induction. 88...
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This note was uploaded on 12/27/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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