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Tentukan jumlah deret geometri berikut .

Tentukan jumlah deret geometri berikut begin mathsize 14px style 1 half plus 1 fourth plus 1 over 8 plus 1 over 16 plus 1 over 32 end style.space

 

Jawaban:

Pada soal suku pertama adalah begin mathsize 14px style 1 half end style, sehingga begin mathsize 14px style a equals 1 half end style. Rasio merupakan perbandingan suku ke-dengan suku ke-(n-1), sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row r equals cell U subscript n over U subscript n minus 1 end subscript end cell row blank equals cell U subscript 2 over U subscript 2 minus 1 end subscript end cell row blank equals cell U subscript 2 over U subscript 1 end cell row blank equals cell fraction numerator begin display style 1 fourth end style over denominator begin display style 1 half end style end fraction end cell row blank equals cell 1 fourth cross times 2 end cell row blank equals cell 1 half end cell end table end style

Ingat rumus jumlah suku ke-deret geometri begin mathsize 14px style S subscript n equals fraction numerator a left parenthesis 1 minus r to the power of n right parenthesis over denominator left parenthesis 1 minus r right parenthesis end fraction comma space r less than 1 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell S subscript 5 equals fraction numerator begin display style 1 half end style open parentheses 1 minus open parentheses begin display style 1 half end style close parentheses to the power of 5 close parentheses over denominator 1 minus open parentheses begin display style 1 half end style close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style open parentheses 1 minus open parentheses begin display style 1 over 32 end style close parentheses close parentheses over denominator begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style cross times open parentheses begin display style 31 over 32 end style close parentheses over denominator begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator begin display style 31 over 64 end style over denominator begin display style 1 half end style end fraction end cell row blank equals cell 31 over 64 cross times 2 end cell row blank equals cell 31 over 32 end cell end table end style

 

Jadi, jumlah deret geometri tersebut adalah begin mathsize 14px style 31 over 32 end style.

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