All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
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

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information