Transcription of Limit sup and limit inf. - 國立臺灣大學
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Limit sup and limit inf. - 國立臺灣大學
Limit sup and Limit order to make us understand the information more on approaches of a given realsequence an n 1 , we give two definitions, thier names are upper Limit and lower Limit . Itis fundamental but important tools in of Limit sup and Limit infDefinition Given a real sequence an n 1 ,wedefinebn sup am:m n andcn inf am:m n .Example 1 1 n n 1 0,2,0,2,.. ,sowehavebn 2andcn 0 for 1 nn n 1 1,2, 3,4,.. ,sowehavebn andcn for n n 1 1, 2, 3,.. ,sowehavebn nandcn for Given a real sequence an n 1 , and thus definebnandcnas the same ,andcn n If there is a positive integerpsuch thatbp , thenbn n there is a positive integerqsuch thatcq , thencn n bn is decreasing and cn is property 3, we can give definitions on the upper Limit and the lower Limit of a givensequence as Given a real sequence an a
Limit sup and limit inf. Introduction In order to make us understand the information more on approaches of a given real sequence an n 1 , we give two definitions, thier names are upper limit and lower limit. It is fundamental but important tools in analysis. Definition of limit sup and limit inf Definition Given a real sequence an n 1
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