Introduction to Infinite Series
Introduction to Infinite Series
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In our eReader you can find the full English version of the book. Read Introduction to Infinite Series Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Introduction to Infinite Series
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13. ^l trencral Tlworem. Ld "o + "i -r he any convergent series of2>ositive and negative terms. Then Lim u^^ = . More generally, Lim [//„ + ?/„ + ! + -f ;'„+, _i] = 0, ra = 00 irJiere ]) is any integer, either constant or varying irilh n.
The proof of this theorem How's directly out of the conception of a limit. Let and plot the points . Sj, . Sg, s^, Then what we mean when we say "x^ approaches a limit U" is that there is a point I about ■which the sja cluster, as n increases. This does not ne...cesi^arily re- quire that (as in the series hitherto eonsideied) s^ should always come steadily nearer to U, as n increases. Thus s.^ may lie further away from [' than . So does. But it does mean that ultimately the sjs will S3 U-c^ s^ U s^U+c^ s, \ \ 1 Mill 1 1 \ — Fk;. 7.
cease to deviate from U liy more than any arbitrarily assigned quan- tity, S, however small. In other words, let 8 be taken at pleasure (rr 1/1, 000, 000, say) and lay off an interval extending to a dis- tance 8 from U in each direction, ((/ — 8, f'-j-8); then for the larger values of ?«, more precisely, for all values of u greatei- than a certain fixed number m, s^ will lie Avithin this interval.
What to read after Introduction to Infinite Series?
You can find similar books in the "Read Also" column, or choose other free books by William F William Fogg Osgood to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
13. ^l trencral Tlworem. Ld "o + "i -r he any convergent series of2>ositive and negative terms. Then Lim u^^ = . More generally, Lim [//„ + ?/„ + ! + -f ;'„+, _i] = 0, ra = 00 irJiere ]) is any integer, either constant or varying irilh n.
The proof of this theorem How's directly out of the conception of a limit. Let and plot the points . Sj, . Sg, s^, Then what we mean when we say "x^ approaches a limit U" is that there is a point I about ■which the sja cluster, as n increases. This does not ne...cesi^arily re- quire that (as in the series hitherto eonsideied) s^ should always come steadily nearer to U, as n increases. Thus s.^ may lie further away from [' than . So does. But it does mean that ultimately the sjs will S3 U-c^ s^ U s^U+c^ s, \ \ 1 Mill 1 1 \ — Fk;. 7.
cease to deviate from U liy more than any arbitrarily assigned quan- tity, S, however small. In other words, let 8 be taken at pleasure (rr 1/1, 000, 000, say) and lay off an interval extending to a dis- tance 8 from U in each direction, ((/ — 8, f'-j-8); then for the larger values of ?«, more precisely, for all values of u greatei- than a certain fixed number m, s^ will lie Avithin this interval.
What to read after Introduction to Infinite Series?
You can find similar books in the "Read Also" column, or choose other free books by William F William Fogg Osgood to read onlineMoreLess
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