已知f(n)=cosnπ/4,求f(1)+f(2)+...+f(100)的值

问题描述:

已知f(n)=cosnπ/4,求f(1)+f(2)+...+f(100)的值
通俗易懂一点,

函数f(n)=cosnπ/4的周期:经观察,知f(1)=f(9)=f(17)=.=f(89)=cos(π/4)=√2/2f(2)=f(10)=f(18)=.=f(90)=cos(2π/4)=0f(3)=f(11)=f(19)=.=f(91)=cos(3π/4)=-√2/2f(4)=f(12)=f(20)=.=f(92)=cos(4π/4)=-1f(5)=-f(1)...