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Tentukan jumlah limit tak hingga deret tersebut

Tentukan jumlah limit tak hingga deret tersebut 

begin mathsize 14px style c. space log space 8 space plus space 1 third log space 2 space plus space 1 over 27 log space 2 space..... end style 

Jawaban:

Mencari rasio 

table attributes columnalign right center left columnspacing 0px end attributes row r equals cell U subscript 3 over U subscript 2 end cell row blank equals cell fraction numerator begin display style 1 over 27 end style log space 2 over denominator begin display style 1 third end style log space 2 end fraction end cell row blank equals cell 1 over 9 end cell end table 

 

Mencari jumlah limit tak hingga

table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript infinity end cell equals cell fraction numerator a over denominator 1 minus r end fraction end cell row blank equals cell fraction numerator log space 8 over denominator 1 minus begin display style 1 over 9 end style end fraction end cell row blank equals cell fraction numerator log space 8 over denominator begin display style 8 over 9 end style end fraction end cell row blank equals cell 9 over 8 log space 2 cubed end cell row blank equals cell 9 over 8.3 space log space 2 end cell row blank equals cell 27 over 8 space log space 2 end cell end table 

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