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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(2): possible method. | Comment 7 of 10 |
(In reply to re: possible method. by Charlie)

The way I did it: (1/2 * 3/4 * ... * 99/100) * (2/3* 4/5...100/101)= 1/101.

The left product is less than the right product, and thus less than sqrt(1/101) which is less than sqrt(1/100) =.1

This is of course very similar to the previous methods given, but I thought I'd write it out so others could see a slight variation.

  Posted by Gamer on 2010-12-14 03:01:04

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