- 719 名前：１３２人目の素数さん mailto:sage [2007/12/31(月) 06:57:34 ]
- >>713
Π[k=1,n] {1 + 4(cos(kπ/(2n+1)))^2} = F[2n+1],
Π[k=1,n] {1 + 4(cos(kπ/(2n+2)))^2} = F[2n+2],
ここに
F[m] = (β^m -α^m)/√5 はフィボナッチ数。
α = (1-√5)/2 = -0.61803398875…
β = (1+√5)/2 = 1.61803398875…
ゆえに
A[n] = F[2n+1]/F[2n+2] → 1/β = |α|. (n→∞)
