M135F08A3 - MATH 135 Fall 2008 Assignment#3 Due Wednesday...

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Unformatted text preview: MATH 135 Fall 2008 Assignment #3 Due: Wednesday 01 October 2008, 8:20 a.m. Hand-In Problems 1. In each part, state the answer. (a) Determine the value of 18 . (b) Determine the value of 19 17 . (c) Determine the value of 9 3 . (d) Determine the value of 12 5 . (e) Write down the expansion of ( x 2- 2 y ) 4 . (f) Determine the coefficient of x 9 in the expansion of (2 x 3- 5) 5 . 2. A sequence of integers is defined by x 1 = 9, x 2 = 3, x m +2 =- x m +1 + 6 x m for m ≥ 1. Prove that x n = 3 · 2 n- (- 3) n for all n ∈ P . 3. A sequence of integers is defined by y 1 = 0, y 2 = 4, y m = 4 y m- 2 for m ≥ 3. Prove that y n = 1 2 (2 n + (- 2) n ) for all n ∈ P . 4. A sequence of integers is defined by t 1 = 3, t 2 = 7, t 3 = 33, t r = 7 t r- 2 + 6 t r- 3 for r ≥ 4. Prove that t n = 2(- 1) n- (- 2) n + 3 n for all n ∈ P . 5. Simplify 5 x 5 + 5 1 x 4 (2- x )+ 5 2 x 3 (2- x ) 2 + 5 3 x 2 (2- x ) 3 + 5 4 x (2- x ) 4 + 5 5 (2- x ) 5 ....
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This note was uploaded on 09/04/2009 for the course MATH 135 taught by Professor Andrewchilds during the Fall '08 term at Waterloo.

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M135F08A3 - MATH 135 Fall 2008 Assignment#3 Due Wednesday...

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