>>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→∞)