Connection Between Sequence and Series

Connection Between Sequence and Series -       ...

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Unformatted text preview:                                               {} ∞ = = {  =    =   + } +   +       +     ∑ =       !     "       #    {} $  = =  ∞ = = { = = = =    } ∑ = ∑ = + + + + +  = = ∑ = =   ∑   +  = ∑ = = + +  +   +    &     &       %       '(             %   ∑ = ∞ = =  →∞ =  ∑ →∞ = )       *  *  *      *     (    +        (  %     ,(        (   (   (     (     "-  ( (    &     .                     /          = )      ( >  − ∑ = = + +  +   + − +           % = ∑ = − = + +  +   + − ,      )      − =   −       !   &  (   !   ⎛ =⎜ ⎝ 0 ∑ = ∑ = − ⎞ =⎟= ⎠ ( + +  +   + − + )−( + +  +   + − ) $      1 $  %   (     %   (                           (                2 %       "            3   (   (       (       →∞ =   (   )   (     %  %     →∞ ( →∞ − − )=  →∞ %   *     →∞   ( − − )= (  −  →∞ − )= − = 4 =  →∞ )       1 +     . 5        (   →∞ = 4 = 4  (   (       &   *        →∞       KDUPLQLF VHULHV  + + ∑ = ∞ =  + = +  +  6      (   (  /   →∞ =  →∞ = 4 % ZH FDQ VKRZ LW GLYHUJHV :DUQLQJ %RULQJ &RQVLGHU ∑ = ∞ = + +  +  + 6 + 7 + 8 + 9 + : + 4 + + + +  + +  + + 6 + + 7 + + ⎞ ⎟+ 7⎠ 0+ /RRNLQJ DW    ⎛ ⎞⎛ ⎞⎛ +⎜ + ⎟+⎜ + + + ⎟+⎜ + + 4 ⎝  ⎠ ⎝ 6 7 8 9⎠ ⎝ : %    HDFK LV ELJJHU WKDQ  %     6 D   (  ( (   (   +    ; )       (       ∑ = ∞ > + ⎛ +⎜ ⎝ ⎞⎛ ⎟+⎜ ⎠⎝ ⎞⎛ ⎟+⎜ ⎠⎝ ⎞ ⎟+ ⎠  )         %               (   ≠4 ⇒ →4 ∑ ∞  ( =       ( <     (  .  <         (      (   (  (     *       ( RI   %   (       $    ]HUR OLPLW IRU WKH VHULHV WR FRQYHUJH %    ( <    LV QRW HQRXJK 7KLQJV   (  ( 2   =   %  3    {} ∞ = = = {  =      + }  ∑ = →∞ + =  ∑ →∞ = +   + =  − ⎛ =⎜ ⎝ = ∑ = ∞ = ∑ = − ∑ = − ⎞ ⎟= ⎠  →4 ≠4 ⇒ ∑ ∞  (   3 = 2     →4 = 4  ...
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This note was uploaded on 12/14/2010 for the course MATH 1za3 taught by Professor Ben during the Winter '10 term at Macalester.

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