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[数列] 一道数列与三角相结合的最值问题

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longma posted 2019-12-26 09:57 |Read mode
Last edited by hbghlyj 2025-4-6 03:42如果方程组 $\left\{\begin{array}{l}\sin x_1+\sin x_2+\cdots+\sin x_n=0 \\ \sin x_1+2 \sin x_2+\cdots+n \sin x_n=2019\end{array}\right.$有实数解,则正整数 $n$ 的最小值是 $\qquad$ .

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facebooker posted 2019-12-27 15:27
\begin{equation}
\left\{
\begin{aligned}
\sin x_1+\sin x_2+\cdots +\sin x_n &=0 \\
\sin x_1+2\sin x_2+\cdots +n\sin x_n  &=2019
\end{aligned}\\
prove:\sin x_1+2\sin x_2+\cdots +n\sin x_n\leqslant [\dfrac{n^2}{4}]
\right.
\end{equation}

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original poster longma posted 2020-1-1 16:22
回复 3# facebooker


“非死不可”大虾,这个怎么证?

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