竞赛习题精选

1.设$x,y,z$是三个复数,定义\[d(x, y)=\frac{|x-y|}{\sqrt{\left(1+|x|^{2}\right)\left(1+|y|^{2}\right)}}.\]求证:\[d(x, y) \leq d(x, z)+d(z, y).\]html 2.设$a_{1}, a_{2}, \cdots, a_{n}$是正实数,求证:\[\sum_{k=1}^{n} a_{k}^

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