若函数f(n)=sinnπ/3,则f(1)+f(2)+……+f(2011)的值为

Question

若函数f(n)=sin nπ/3,则f(1)+f(2)+……+f(2011)的值为

Answer 1

sinπ/3+sin2π/3+sin3π/3+sin4π/3+sin5π/3+sin6π/3=0
6项和为0
2011=335*6+1
原式=f(1)=sinπ/3=√3/2