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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(3): possible method. =almost like Sofia SPOILER | Comment 9 of 10 |
(In reply to re(2): possible method. by Gamer)

The way Sofia did it:

Let p'=2/3* 4/5..    *96/97*98/99*1 .

Since 2/3>1/2,  4/5>3/4    ...   98/99>97/98   and 1>99/100

and      p*p'= 1/100= (.1)*(.1)     


  SO  p   IS LESS YHAN 1/10.

  Posted by Ady TZIDON on 2010-12-14 07:51:04
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