"Let (a_n) be bounded decreasing and (b_n) be bounded increasing sequences. Let x_n =a_n+b_n. Show that [tex]\sum|x_n-x_{n+1}|[/tex] converges."(adsbygoogle = window.adsbygoogle || []).push({});

This ALMOST is a telescoping sum, but it doesn't work since if I try to use the triangle inequality, the sum I want is on the greater side. Ratio test, root test, etc all fail since there is insufficient information.

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# Telescoping Sum

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