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assig3

assig3 - 3 for all n ≥ 1(b Find a closed form formula for...

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MATH 135 Algebra, Assignment 3 Due: Wed Oct 7, 8:30 am 1: (a) Let a 1 = 1 and a n +1 = 3 a n + 2 for n 1. Show that a n = 2 · 3 n - 1 - 1 for all n 1. (b) Let a 1 = 3 and a n +1 = 2 a n - 1 for n 1. Find a closed form formula for a n . (c) Let a 1 = 2 and a n +1 = 5 a n - 4 a n for n 1. Show that 1 a n a n +1 4 for all n 1. 2: (a) Let a 0 = 0 and a 1 = 1 and for n 2 let a n = a n - 1 + 6 a n - 2 . Show that we have a n = 1 5 ( 3 n - ( - 2) n ) for all n 0. (b) Let a 0 = 1 and a 1 = 1 and for n 2 let a n = 2 a n - 1 + a n - 2 . Show that we have a n = 1 2 ( (1 + 2) n + (1 - 2) n ) for all n 0. 3: (a) Show that n X i =1 (2 i
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Unformatted text preview: 3 for all n ≥ 1. (b) Find a closed form formula for n X i =1 (-1) i (2 i-1) 2 for n ≥ 1. 4: (a) Expand (2 x + 5) 4 . (b) Expand ( x-1 2 x ) 8 . (c) Find the term involving x 8 in the expansion of ± x 3 6-12 x 2 ² 11 . 5: (a) Evaluate n X i =0 ± n i ² 1 2 i . (b) Evaluate n X i =0 ³ 2 n 2 i ´ 1 2 i . (c) Evaluate n X i =0 ³ n + i i ´ 1 2 i ....
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