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Hail to thee, Sofia! (Posted on 2010-12-13) Difficulty: 2 of 5


Let p= 1/2*3/4*5/6*7/8..*99/100.

Is p bigger than, equal to or less than 0.1 ?

The famous Sofia Kovalevskaya (1850-1891) solved this problem allegedly in no time, when she was only twelve years old.

Please provide your answer without programming and without direct evaluation.

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: What does not work... | Comment 6 of 10 |
(In reply to What does not work... by Jer)

I don't believe what Ady found is the mistake -- you are not subtracting infinite terms anywhere.

The issue I found is your approximation is off by O(log(n)), which is usually not a problem. In this case when you write ln(p) = 0 + O(ln(50)), taking the exponential of both sides gives p = O(50).

So P is off by a factor of 50, which removes any meaningful information.

  Posted by Gamer on 2010-12-14 02:54:49

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