# dm-lec23-recur2 - Recurrence Relations Recurrence Relations...

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Recurrence Relations Chapter 7 p (7.2 Solving Recurrence Relations) ovember 2, 2009 November 2, 2009 Recurrence Relations • A recurrence relation for the sequence a 0 , a 1 , … is an quation that relates a certain of its predecessors equation that relates a n to certain of its predecessors a 0 , a 1 , …, a n-1 . • Initial conditions for the sequence a , a , … are q 0 , 1 , explicitly given values for a finite number of the terms of the sequence. • To solve a recurrence relation = to find an explicit formula for the general term a n – By applying iteration t hd l id l i h lt i – Method applied linear homogenous recurrence relations with constant coefficients – Using generating functions [email protected] CS204 Discrete Math (Fall 2009) 2 Example 7.1.3 • Invest \$1000 at 12 percent interest compounded annually. Let A n : amount at the end of n years. Find a recurrence relation and initial conditions at define the sequence {A that define the sequence {A n } = A (0 12)A =112A n A n A n-1 + (0.12)A n-1 1.12 A n-1 , n 1. – Initial condition: A 0 = 1000. –A n = (1.12) A n-1 = (1.12) [(1.12) A n-2 ] = (1.12) 2 A n-2 (1 12) 1 12) A = (1 12) = (1.12) 2 [(1.12) A n-3 ] = (1.12) 3 A n-3 = …. = (1.12) n (1000) [email protected] CS204 Discrete Math (Fall 2009) 3 Example 7.2.4 • Minimum number of moves for

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## This note was uploaded on 02/04/2010 for the course COMPUTER S Cs206 taught by Professor Unkown during the Spring '08 term at Korea Advanced Institute of Science and Technology.

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dm-lec23-recur2 - Recurrence Relations Recurrence Relations...

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