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Tentukan jumlah  suku pertama dari barisan geometri

Pertanyaan

Tentukan jumlah begin mathsize 14px style 15 end style suku pertama dari barisan geometri begin mathsize 14px style 1 fourth plus 1 over 8 plus 1 over 16 plus... end style 

Pembahasan Soal:

Dari deret tersebut diketahui 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight a equals cell 1 fourth end cell row blank blank blank row straight r equals cell fraction numerator begin display style 1 over 8 end style over denominator begin display style 1 fourth end style end fraction end cell row blank equals cell fraction numerator 1 cross times 4 over denominator 8 cross times 1 end fraction end cell row blank equals cell 4 over 8 end cell row blank equals cell 1 half end cell end table end style

Maka jumlah begin mathsize 14px style 15 end style suku pertama begin mathsize 14px style open parentheses straight n equals 15 close parentheses end style adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight S subscript straight n end cell equals cell fraction numerator straight a open parentheses 1 minus straight r to the power of straight n close parentheses over denominator 1 minus straight r end fraction end cell row blank equals cell fraction numerator begin display style 1 fourth end style open parentheses 1 minus open parentheses begin display style 1 half end style close parentheses to the power of 15 close parentheses over denominator 1 minus begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator begin display style 1 fourth end style open parentheses 1 minus begin display style fraction numerator 1 over denominator 32.768 end fraction 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 1 fourth end style open parentheses begin display style fraction numerator 32.767 over denominator 32.768 end fraction end style close parentheses over denominator begin display style 1 half end style end fraction end cell row blank equals cell 1 half open parentheses fraction numerator 32.767 over denominator 32.768 end fraction close parentheses end cell row blank equals cell fraction numerator 32.767 over denominator 65.536 end fraction end cell end table end style 

Jadi jumlah undefined suku pertama deret tersebut adalah begin mathsize 14px style fraction numerator 32.767 over denominator 65.536 end fraction end style

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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