Is the following statement true? C>0 and t>0 are positive real numbers. For every positive integer n, there exist positive real numbers 0 < r_1 < ... < r_n and positive real numbers 0 < a_1 < ... < a_n such that (i) (a_i-r_1)^2...(a_i-r_n)^2 > Ca_i^{2n} for i=1,...,n (ii) t < a_1 < r_1 and r_{i-1} < a_i < r_i for i=2,...,n Answer: (A) It's true for all n (B) It's not true Pick (A) or (B). [edited by - a7h3iz7 on January 12, 2003 6:30:42 PM]

Stumped on yer homework, huh?

God was my co-pilot but we crashed in the mountains and I had to eat him...

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Original post by Landsknecht
Stumped on yer homework, huh?

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This is not a homework problem. I am not looking for proof. I just need the answer (A) or (B).

[edited by - a7h3iz7 on January 12, 2003 6:37:54 PM]

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Original post by a7h3iz7

This is not a homework problem. I am not looking for proof. I just need the answer (A) or (B).

[edited by - a7h3iz7 on January 12, 2003 6:37:54 PM]

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Mind if I ask why this problem interests you so if it''s not homework (or review for a test or similar)?

If it were on a test I would guess that it is false, although I only barely passed my discrete mathmatics course.

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Original post by a7h3iz7
This is not a homework problem. I am not looking for proof. I just need the answer (A) or (B).

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If this is not a homework problem, could you please describe the context in which this question arose? Without such, we are forced to believe that you are merely asking for an answer to your homework and will treat your enquiry accordingly.

Before asking for further help, you might want to consider the series expansion of the left hand side of the first equation, for various values of n. That may not lead to an answer, but it's where I would begin.

Cheers,

Timkin

[edited by - Timkin on January 12, 2003 7:04:38 PM]