Let be a non-increasing non-negative sequence. Prove that is bounded and that I would appreciate any help.
Last edited by JoachimAgrell; Jan 28th 2010 at 06:13 PM.
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Originally Posted by JoachimAgrell Let be a non-increasing non-negative sequence. Prove that is bounded and that I would appreciate any help. Maybe I'm reading this wrong but what about , it's clearly non-increasing and non-negative but which is clearly not bounded
Oops. I meant (-1)^{i+1} in that series.
Originally Posted by JoachimAgrell Let be a non-increasing non-negative sequence. Prove that is bounded and that I would appreciate any help. Okay here's my attempt: By induction we prove that and thus we get that is bounded because it's non negative. Now it's clear that for all and since each of these are monotonic we get that has at most two acc. points and so and but
Last edited by Jose27; Jan 28th 2010 at 08:19 PM.
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