競賽習題精選

1.設$x,y,z$是三個複數,定義\[d(x, y)=\frac{|x-y|}{\sqrt{\left(1+|x|^{2}\right)\left(1+|y|^{2}\right)}}.\]求證:\[d(x, y) \leq d(x, z)+d(z, y).\]html 2.設$a_{1}, a_{2}, \cdots, a_{n}$是正實數,求證:\[\sum_{k=1}^{n} a_{k}^

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