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若f(x)=sin(∏x/3),则f(1)+f(2)+f(3)+...+f(2003)=
人气:273 ℃ 时间:2020-05-08 17:48:13
解答
当x=6k-5,(k∈N※,下同).则f(6k-5)=sin(2kπ-5π/3)=-sin(5π/3)=√3/2.f(6k-4)=sin(2kπ-4π/3)=√3/2f(6k-3)=sin(2kπ-3π/3)=0f(6k-2)=sin(2kπ-2π/3)=-√3/2f(6k-1)=sin(2kπ-π/3)=-√3/2f(6k)=sin2kπ=0.∴f(...
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