函数f(x)=sinπ/4×x,求f(1)+……+f(20)的值

Question

函数f(x)=sinπ/4×x,求f(1)+……+f(20)的值

Answer 1

f(1)=sinπ/4
f(2)=sinπ/2=1
f(3)=sin3π/4=sinπ/4
f(4)=sinπ=0
f(5)=sin5π/4=-sinπ/4
f(6)=sin3π/2=-1
f(7)=sin7π/2=-sinπ/4
f(8)=sin2π=0
f(9)=sin9π/4=sinπ/4 所以可得8为周期,每个周期和为0
f(1)+……+f(20)
=3x0+f(1)+f(2)+f(3)+f(4)
=1+√2