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.

(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