Find the sum of the fiftieth powers of all sides and diagonals of a regular 100-gon inscribed in a circle of radius R.

(In reply to

halfway through the general solution by Michael Kornrade)

I repeat the two important formulas:

Sv = (2*R)^p * SUM( [sin( k * pi / N)]^p ) for k = 0...N-1

S = N * Sv / 2

For the moment, I cannot make the formula more compact, for p > 2...

Go to http://mathworld.wolfram.com/Sine.html to find compact formulas for p = 1 (eq.16 or eq.21) and p = 2 (eq.20).

So, in a Matlab computation for N = 100, p = 50 and R = 0.5 I get:

Sv = 11.2275172659217...

S = 561.375863296086...

*Edited on ***January 10, 2013, 7:09 pm**

*Edited on ***January 10, 2013, 7:12 pm**