已知f(n)=sinnπ/4,n∈Z.求f(1)+f(2)+……f(2010)

解： f(n)=sinnπ/4 函数的周期是8 f(1)+f(2)+…+f(8)=sinπ/4+sin2π/4+sin3π/4+sin4π/4+sin5π/4+sin6π/4+sin7π/4+sin8π/4=0 f(1)+f(2)+…+f(2010) = 251x[f(1)+f(2)+…+f(8)]+ =sin(502π+π/4)+sin(502π+π/2) =√2/2+1 =(2+=2)