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

Home > Numbers
Front to back (Posted on 2007-03-18) Difficulty: 3 of 5
Suppose one sequence is formed by multiplying termwise the sequence 1,2,...n by the sequence n,n-1,...1 and another sequence is formed by multiplying termwise the sequence 2,4,...n by the sequence 2,4,...n.

Show that for even n, the sum of each sequence is the same.

No Solution Yet Submitted by Gamer    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Lots of summing | Comment 1 of 3
Writing n=2K, the first sum is the sum for I=1 to K of I times (2K+1-I), or (2K+1) times the sum of all numbers from 1 to 2K, minus the sum of the squares of all numbers from 1 to 2K, which eventually works out to 2/3.K.(K+1).(2K+1).

The second sum is 4 times the sum of squares of the numbers from 1 to K, which comes out to the same value.

  Posted by Old Original Oskar! on 2007-03-18 13:14:50
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 (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information