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April 22nd, 2012, 02:39 AM  #1 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Which one is bigger?
[attachment=0:3o87a6ix]which one is bigger.jpg[/attachment:3o87a6ix] Sorry for bothering! Albert 
April 22nd, 2012, 06:43 AM  #2 
Senior Member Joined: Dec 2011 Posts: 277 Thanks: 1  Re: Which one is bigger?
Interesting. But imho, I think the difference between A and B is huge. I'll show you my solution, but only after I finish watching one of my favorite tv series: Touch  by Kiefer Sutherland. 
April 22nd, 2012, 08:43 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,296 Thanks: 934  Re: Which one is bigger?
It sure is huge: 315 ...... 125 ; 80 digits! "divisions" start off this way: 1/2, 3/8, 5/16, 35/128 .... ...back to the hockey game... 
April 22nd, 2012, 09:50 AM  #4 
Senior Member Joined: Dec 2011 Posts: 277 Thanks: 1  Re: Which one is bigger?
We're given But we know that the product of positive odd/even integers can be rewritten as where k=50 I then take the natural log of both sides to obtain Now I substitute k=50 into the above equation to get Last, I compare the value of A to the value of B (which is 0.1). Obviously, B is larger than A. Now that I see the remark given by Denis, I believe we solve this problem in different way. 
April 24th, 2012, 02:43 AM  #5 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: Which one is bigger?
[attachment=0:194zisrt]B is bigger.jpg[/attachment:194zisrt]

April 24th, 2012, 02:49 AM  #6 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Which one is bigger?
Is it possible to prove (or disprove) that A < 1/5 ???

April 24th, 2012, 03:49 AM  #7 
Senior Member Joined: Dec 2011 Posts: 277 Thanks: 1  Re: Which one is bigger?
Well done, Albert! Look at my solution again I understand that there is no reason to find the exact value for A. I even think on how to approximate by using Stirling approximation... 
April 24th, 2012, 03:53 AM  #8  
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: Which one is bigger? Quote:
since A<B=1/10, A must be less than 1/5.  
April 24th, 2012, 04:17 AM  #9 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Which one is bigger?
Thanks, albert. Now for another solution to this problem. I'm logging out now, and will tell you the method a few hours later. 

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