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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    
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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

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