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Hitung jumlah kesepuluh dari deret-deret geometri ...

Hitung jumlah kesepuluh dari deret-deret geometri berikut:

a. begin mathsize 14px style 300 plus open parentheses negative 150 close parentheses plus 75 plus horizontal ellipsis end style 

 

Jawaban:

begin mathsize 14px style 300 plus open parentheses negative 150 close parentheses plus 75 plus horizontal ellipsis end style

Diketahui :

begin mathsize 14px style a equals 300 r equals U subscript 2 over U subscript 1 equals fraction numerator negative 150 over denominator 300 end fraction equals negative 1 half end style

Ditanyakan: begin mathsize 14px style S subscript 10 ? end style 

Jawab:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript n end cell equals cell fraction numerator a open parentheses 1 minus r to the power of n close parentheses over denominator 1 minus r end fraction end cell row cell S subscript 10 end cell equals cell fraction numerator 300 open parentheses 1 minus open parentheses negative begin display style 1 half end style close parentheses to the power of 10 close parentheses over denominator 1 minus open parentheses negative 1 half close parentheses end fraction end cell row blank equals cell fraction numerator 300 open parentheses 1 minus begin display style 1 over 1024 end style close parentheses over denominator begin display style 3 over 2 end style end fraction end cell row blank equals cell fraction numerator 300 open parentheses begin display style 1024 over 1024 minus 1 over 1024 end style close parentheses over denominator 3 over 2 end fraction end cell row blank equals cell fraction numerator 300 open parentheses begin display style 1023 over 1024 end style close parentheses over denominator 3 over 2 end fraction end cell row blank equals cell fraction numerator 306.900 over denominator 1024 end fraction divided by 3 over 2 end cell row blank equals cell fraction numerator 306.900 over denominator 1024 end fraction cross times 2 over 3 end cell row blank equals cell fraction numerator 102.300 over denominator 512 end fraction end cell row blank equals cell 199 412 over 512 end cell row blank equals cell 199 103 over 128 end cell end table end style  

Jadi, jumlah kesepuluh dari begin mathsize 14px style bold 300 bold plus bold left parenthesis bold minus bold 150 bold right parenthesis bold plus bold 75 bold plus bold horizontal ellipsis end style  adalah begin mathsize 14px style bold 199 bold 103 over bold 128 end style.

 

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