How to prove that these are Cauchy sequences? – math.stackexchange.com

How to prove that these are Cauchy sequences? – math.stackexchange.com

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Let $x_1,x_2,x_3,\dots$ is a non-decreasing and $y_1,y_2,y_3,\dots$ is a non-increasing sequence, and they are real sequences. If $|x_n-y_n|\le\frac{|x_1-y_1|}{2^n}$ for each $n\in \Bbb N$, then show ...

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