6SeriesWecallanormedspace(X;kk)aBanachspaceprovidedthateveryCauchyseq - PDF document

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6SeriesWecallanormedspace(X;kk)aBanachspaceprovidedthateveryCauchyseq - PPT Presentation

kk11nXk21 k11 k111 n2SothesequencesnofpartialsumsisboundedinRandsinceitisalsoincreasingitconvergesExample65TheharmonicseriesP1kdivergesIndeedifsnPnk11kthenjs2nsnj1 n1 ID: 248106

k(k1)=1+nXk=21 k11 k=1+11 n2:So thesequence(sn)ofpartialsumsisboundedinRandsinceitisalsoincreasing itconverges.Example6.5.TheharmonicseriesP1=kdiverges.Indeed ifsn=Pnk=11=k thenjs2nsnj=1 n+1+::

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6SeriesWecallanormedspace(X;kk)aBanachspaceprovidedthateveryCauchyseq - PDF document

6SeriesWecallanormedspace(X;kk)aBanachspaceprovidedthateveryCauchyseq - PPT Presentation

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