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Unformatted text preview: , S 2 , S 3 , ... Question #7. 1 (a) Solve the recurrence relation a n = a n1 + 1 + 2 n1 subject to the initial condition a = 1. (b) Solve the recurrence relation a n = 2 a n1 − 5 a n2 subject to the initial conditions a = 4, a 1 = 4. Question #8. Consider the following useless algorithm: 1 . procedure foo ( n ) 2 . if n = 1 then 3 . return 4 . x := x + 1 5 . m := ⌊ n/ 2 ⌋ 6 . call foo ( m ) 7 . if n is even then 8 . call foo ( m ) 9 . else 10 . x := x + 1 11 . end foo Let b n denote the number of times the statement x := x + 1 is executed. (a) Determine a recurrence relation and initial conditions for the sequence { b n } . (b) Solve the recurrence relation in case n is a power of 2. Extra Credit. Using some calculus if necessary, Fnd a simpliFed expression for n ∑ k =1 k 2 2 k . 2...
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 Spring '08
 WOUTERS
 Math, Algebra, Set Theory, Recurrence relation, Fibonacci number

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