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

Home > Just Math
Rooted to the Floor II (Posted on 2014-09-08) Difficulty: 3 of 5
Define F(x) = floor(4√x).

Find the value of :

1/F(1) + 1/F(2) +....+ 1/F(2014)

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Pencil and paper solution | Comment 2 of 3 |
1^4 = 1
2^4 = 16
3^4 = 81
4^4 = 256
5^4 = 625
6^4 = 1296
7^4 = 2401

So there are 15 terms equal to 1/1, (81-16) terms equal to 1/2, etc.

Final answer = 

(16-1)/1 + (81-16)/2 + (256-81)/3 + (625-256)/4 + (1296 - 625)/5 + (2015 - 1296)/6 = 27127/60, which is approx 452.11667 

  Posted by Steve Herman on 2014-09-08 22:00:55
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 (4)
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