hw09 - a 1 = a 2 = 1 a n +1 = a n + 2 a n-1 , for n 2 . a....

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Intro to Abstract Math Homework 9 Fall 2009 Due September 25 Exercise 25. Verify the following claims made in class. a. For all n N and all 1 k n ± n + 1 k ² = ± n k ² + ± n k - 1 ² . b. For all n,l N l ( l + 1) ··· ( l + ( n - 1)) = n ! ± n + l - 1 l - 1 ² . Exercise 26. Prove that for all n N 2( n + 1 - 1) < 1 + 1 2 + ··· + 1 n . Exercise 27. Define a sequence of integers recursively by
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Unformatted text preview: a 1 = a 2 = 1 a n +1 = a n + 2 a n-1 , for n 2 . a. Write out the rst 8 terms of the sequence. b. Guess an explicit formula for a n . Hint: Multiply the numbers you found in part ( a ) by 3. c. Prove that your formula is correct....
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This note was uploaded on 02/29/2012 for the course MATH 3326 taught by Professor Ryandaileda during the Fall '09 term at Trinity University.

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