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

Home > Just Math
An extended harmony (Posted on 2011-11-01) Difficulty: 3 of 5
How many members of the harmonic series 1+1/2+1/3+1/4+ …+1/n are needed to add up close to 10 , without going over it?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
A simple upper bound | Comment 1 of 5
Writing a program would not be much of a challenge even for me so I thought Id see what I can do with p&p.

The classic proof that the harmonic series diverges is useful.

round each term whose denominator is not a power of 2 down so that it is.  1/3 becomes 1/4.  1/5, 1/6, and 1/7 become 1/8 etc.  This creates a smaller sequence.

Now there are two 1/4s which add to 1/2,  there are four 1/8s which add to 1/2 etc.

Since the first term is 1, you will need 18 of these 1/2s, the last one being from a bunch of 1/2^18

So if you have 2^18 = 262144 terms it will definitely be over 10.

  Posted by Jer on 2011-11-01 10:19:57
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information