AP 04 - Jan 25

# AP 04 - Jan 25 - a n < 4 n for n 1 . 6. Let a n be dened...

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1 Math 2602 M1/M2 Spring 2007 Additional Problems 4 Ceiling, Floor Functions and Induction 1 Thursday, Jan 25th 1. Find formula for a n = a d n/ 2 e + a b n/ 2 c , n 2 , a 1 = 1 . 2. Show that b log 2 (2 n ) c = b log 2 (2 n + 1) c holds true for all n 1 . 3. Use the Principle of Mathematical Induction to show that a n = b log 2 n c satisﬁes a n = a d n/ 2 e + 1 , n 2 , a 1 = 0 . 4. Use the Principle of Mathematical Induction to show that a n = d log 2 n e satisﬁes a n = 1 + a b n/ 2 c , n 2 , a 1 = 0 . 5. Let a n be deﬁned recursively by a n = n + a b n/ 3 c + a b n/ 5 c + a b n/ 7 c , n 1 , a 0 = 0 . Use the Principle of Mathematical Induction to show that
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Unformatted text preview: a n < 4 n for n 1 . 6. Let a n be dened recursively by a n = 1 + max { a b n/ 2 c , a d n/ 2 e } , n 2 , a = a, a 1 = b. Use the Principle of Mathematical Induction to show that if a < b, then a n is an increasing sequence n . 1 T. Yolcu, School of Mathematics at Georgia Tech. Email: tyolcu@math.gatech.edu ....
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## This note was uploaded on 05/12/2010 for the course MATH 2602 taught by Professor Costello during the Spring '09 term at Georgia Institute of Technology.

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