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

Home > Shapes
Summing the fiftieth power (Posted on 2012-11-29) Difficulty: 5 of 5
Find the sum of the fiftieth powers of all sides and diagonals of a regular 100-gon inscribed in a circle of radius R.

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts possible approach | Comment 1 of 3

Let R=1/2 (so the diagonals = 1)

Then the sum is 50+[100*sin(pi/100)^50], with the expression in square brackets being of the order of 10^-76. It's not obvious to me how these highly incommensurate numbers could be added with any meaningful exactitude.

This difficulty is further enhanced if the 'proper diagonals' (i.e. including all those not passing though the centre) are taken since there are 4850 of those, and they are of varying lengths.



Edited on December 11, 2012, 2:12 am
  Posted by broll on 2012-11-30 04:52:27

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 (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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