若f(n)=sin(nπ/6)(n∈Z),则f(1)+f(3)+f(5)+……+f(119)=

Question

若f(n)=sin(nπ/6)(n∈Z),则f(1)+f(3)+f(5)+……+f(119)=

Answer 1

f(1)+f(3)+f(5)+f(7)+f(9)+f(11)=sin(π/6)+sin(3π/6)+sin(5π/6)+sin(7π/6)+sin(9π/6)+sin(11π/6)
=0
1,3,5,7,9,11一共6个
1,3,119 一共60个
f(n)=sin(nπ/6) 是 周期函数
f(1)+f(3)+f(5)+……+f(119)=10(f(1)+f(3)+f(5)+f(7)+f(9)+f(11))=10*0=0