XCAS wins

[Albert Chan]

It seems this always work ... Can anyone prove it ?

p(n) := {local k; product(sin(k/n * pi/2), k, 1, n-1)}

Prove p(n) = √(n) / 2^n-1

Example:
p(2) = sin(pi/2) = √(2) / 2¹
p(3) = sin(1/3 pi/2) sin(2/3 pi/2) = (1/2)(√(3)/2) = √(3)/2²
p(4) = sin(1/4 pi/2) sin(2/4 pi/2) sin(3/4 pi/2) = 1/4 = √(4)/2³

And, the one from first post: p(107) = √(107)/2¹⁰⁶

Update: got the proof online: https://math.stackexchange.com/questions...ect=1&lq=1