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Topic: An Atypical Evaluation (Read 814 times) |
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K Sengupta
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An Atypical Evaluation
« on: Feb 19th, 2006, 11:36pm » |
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Consider two functions F(x) and G(y) such that:
F(x) = 1/3 + 1/7 + 1/15 + .................+ 1/( 2 x+1 -1) , and
G(y) = 1/5 + 1/17 + ..............+ 1/(12y-7)
Let F8(x) and G8(y) respectively denote the values of F(x) and G(y) rounded off to 8 places of decimals.
Determine the minimum value of m and n ( where m and n are whole numbers) such that:
F8(m) = G8(n).
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Barukh
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Re: An Atypical Evaluation
« Reply #1 on: Feb 21st, 2006, 6:28am » |
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Does rounding off means that |F(x) - F8(x)| <= 5*10-9?
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towr
wu::riddles Moderator
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Some people are average, some are just mean.
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Re: An Atypical Evaluation
« Reply #2 on: Feb 21st, 2006, 6:49am » |
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on Feb 19th, 2006, 11:36pm, K Sengupta wrote:Determine the minimum value of m and n ( where m and n are whole numbers) such that:
F8(m) = G8(n). |
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My guess is no such pair m and n exists, except for when both are 0 (an empty sum in both cases).
Of course there is always the possibility my program to find them is flawed, machine error maybe..
There's no improvement from F8(28)=0.60669515, G8(127)=0.60733037 onwards.. F8 doesn't increase in value anymore..
btw, the minimum distance between f and g along the way is 0.00000654867
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| « Last Edit: Feb 21st, 2006, 7:12am by towr » |
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