f(n)=sin nπ/6 ,求f(1)+f(2)+……+f(100)的值,π是pai

来源:学生作业学帮网 编辑:学帮网 时间:2024/05/16 09:26:00

f(n)=sin nπ/6 ,求f(1)+f(2)+……+f(100)的值,
π是pai

∵f(13)=sin(13π/6)=sin(2π+π/6)=sin(π/6)=f(1) ∴f(1)=f(1+12×k)
∵f(7)=sin(7π/6)=sin(π+π/6)=﹣sin(π/6)=﹣f(1) ∴f(1)+f(1+6m)=0
∴f(1)+f(2)+……+f(100)=8×[f(1)+f(2)+•••+f(12)]+f(99)+f(100)
=8×0+sin(33π/2)+sin(50π/3)
=sin(π/2)+sin(2π/3)
=1+√3/2