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Unformatted text preview: d , and let b 1 ,...,b n ,... be a geometric progression with a positive ratio r . Prove that there exist numbers x and y such that b n = xy a n for all n ≥ 1. 5. Assume that the numbers x 1 ,x 2 ,...,x n are all non-zero and form an arithmetic progres-sion. Show that 1 x 1 x 2 + ··· + 1 x n-1 x n = n-1 x 1 x n for any n ≥ 2. 6. Bonus Question If the equality above is true for all n ≥ 2, does it imply that the sequence ( x n ) n ≥ 1 is an arithmetic progression ?...
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This note was uploaded on 12/07/2011 for the course MATH 245 taught by Professor Cioaba during the Fall '10 term at University of Delaware.
- Fall '10