◆ わからない問題はここに書いてね １７９ ◆

>>229,246,273,282
和積公式により
　sin(2πk/n)cos(3πk/n) = (1/2){sin(5πk/n) - sin(πk/n)}.
与式 = (1/2π^2)Lim(n→∞) Σ[k=1,n] (π+ πk/n){sin(5πk/n) - sin(πk/n)}(π/n).
　= (1/(2π^2))∫_[0,π] (π+x){sin(5x) - sin(x)} dx
　= (1/(2π^2)) [ (π+x){-(1/5)cos(5x) +cos(x)} + ∫_[0,π] {(1/5)cos(5x) -cos(x)}dx ]
　= (1/(2π^2)) [ (π+x){-(1/5)cos(5x) +cos(x)} + (1/25)sin(5x) -sin(x) ](x=0,π)
　= (1/(2π^2)) [ (π+x){-(1/5)cos(5x) +cos(x)} ](x=0,π)
= -6/(5π)
　≒ -0.381971863420549･･･.