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April 22nd, 2012, 02:39 AM   #1
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Which one is bigger?

[attachment=0:3o87a6ix]which one is bigger.jpg[/attachment:3o87a6ix]



Sorry for bothering!

Albert
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April 22nd, 2012, 06:43 AM   #2
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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.
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April 22nd, 2012, 08:43 AM   #3
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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...
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April 22nd, 2012, 09:50 AM   #4
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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.
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April 24th, 2012, 02:43 AM   #5
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Re: Which one is bigger?

[attachment=0:194zisrt]B is bigger.jpg[/attachment:194zisrt]
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April 24th, 2012, 02:49 AM   #6
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Re: Which one is bigger?

Is it possible to prove (or disprove) that A < 1/5 ???
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April 24th, 2012, 03:49 AM   #7
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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...
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April 24th, 2012, 03:53 AM   #8
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Re: Which one is bigger?

Quote:
mathbalarka said: Is it possible to prove ( or disprove) that A < 1/5 ???
Of course:
since A<B=1/10,
A must be less than 1/5.
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April 24th, 2012, 04:17 AM   #9
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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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