分类：教育/科学-学习帮助
问题：高一数学填空题2已知f(x)=cosxπ/5(x∈N+),则f( 
已知f(x)=c xπ/5 (x∈N+),则f(1)+f(2)+…+f(2000)=_________________-
回答：f(x) = cos(xπ/5);

cos(1π/5)+ cos(2π/5)+ ... + cos(10π/5) = 0;

cos(2kπ + 1π/5)+ cos(2kπ+2π/5)+ ... + cos(2kπ+10π/5) = 0;
k = 1,2,...

f(1)+f(2)+...+f(2000)
=f(1)+f(2)+...+f(10)
 +f(11)+f(12)+...+f(20)
 +...
 +f(1991)+f(1992) + ...+ f(2000)
=0.