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@ -515,9 +515,9 @@ $$|x_{n+1} - x_n| \leq r |x_n - x_{n-1}| \leq r^2 |x_{n-1} - x_{n-2}| \leq \cdot
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于是对任意正整数 $m > n$，有
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$$
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\begin{aligned}
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|x_m - x_n| &\leq |x_m - x_{m-1}| + |x_{m-1} - x_{m-2}| + \cdots + |x_{n+1} - x_n| \\
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&\leq (r^{m-2} + r^{m-3} + \cdots + r^{n-1}) |x_2 - x_1| \\
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&= r^{n-1} \cdot \frac{1 - r^{m-n}}{1 - r} \cdot |x_2 - x_1| \\
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|x_m - x_n| &\leq |x_m - x_{m-1}| + |x_{m-1} - x_{m-2}| + \cdots + |x_{n+1} - x_n| \\[1em]
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&\leq (r^{m-2} + r^{m-3} + \cdots + r^{n-1}) |x_2 - x_1| \\[1em]
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&= r^{n-1} \cdot \frac{1 - r^{m-n}}{1 - r} \cdot |x_2 - x_1| \\[1em]
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&\leq \frac{r^{n-1}}{1 - r} |x_2 - x_1|.
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\end{aligned}
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$$
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