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        riddles >> hard >> An Atypical Evaluation
        
(Message started by: K Sengupta on Feb 19^th, 2006, 11:36pm)

Title: An Atypical Evaluation
Post by K Sengupta on Feb 19^th, 2006, 11:36pm

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).

Title: Re: An Atypical Evaluation
Post by Barukh on Feb 21^st, 2006, 6:28am

Does rounding off means that |F(x) - F8(x)| <= 5*10^-9?

Title: Re: An Atypical Evaluation
Post by towr on Feb 21^st, 2006, 6:49am

on 02/19/06 at 23:36:40, K Sengupta wrote:

Determine the minimum value of m and n ( where m and n are whole numbers) such that:

F8(m) = G8(n).

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