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Hitunglah jumlah begin mathsize 14px style 7 end style suku pertama deret geometri begin mathsize 14px style 1 third plus 1 over 9 plus 1 over 27 plus horizontal ellipsis end style .

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Jawaban

jumlah begin mathsize 14px style 7 end style suku pertama deret geometri begin mathsize 14px style 1 third plus 1 over 9 plus 1 over 27 plus horizontal ellipsis end style sama dengan begin mathsize 14px style fraction numerator 1.093 over denominator 2.187 end fraction end style.

Pembahasan

Perhatikan deret geometri begin mathsize 14px style 1 third plus 1 over 9 plus 1 over 27 plus horizontal ellipsis end style . Diketahui suku pertama deret itu adalah

begin mathsize 14px style U subscript 1 equals italic a equals 1 third end style

dan rasionya adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row italic r equals cell U subscript 2 over U subscript 1 end cell row blank equals cell fraction numerator begin display style 1 over 9 end style over denominator begin display style 1 third end style end fraction end cell row blank equals cell 1 over up diagonal strike 9 cubed cross times up diagonal strike 3 to the power of 1 over 1 end cell row blank equals cell 1 third end cell end table end style

Karena Error converting from MathML to accessible text. maka

begin mathsize 14px style S subscript n equals fraction numerator italic a left parenthesis italic 1 italic minus sign italic r to the power of n right parenthesis over denominator italic 1 italic minus sign italic r end fraction end style

sehingga jumlah begin mathsize 14px style 7 end style suku pertamanya adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript 7 end cell equals cell fraction numerator begin display style 1 third end style middle dot open parentheses 1 minus sign open parentheses begin display style 1 third end style close parentheses to the power of 7 close parentheses over denominator 1 minus sign begin display style 1 third end style end fraction end cell row blank equals cell fraction numerator begin display style 1 third end style middle dot open parentheses 1 minus sign begin display style fraction numerator 1 over denominator 2.187 end fraction end style close parentheses over denominator begin display style 2 over 3 end style end fraction end cell row blank equals cell 1 over up diagonal strike 3 to the power of 1 middle dot open parentheses fraction numerator 2.187 minus sign 1 over denominator 2.187 end fraction close parentheses middle dot up diagonal strike 3 to the power of 1 over 2 end cell row blank equals cell fraction numerator up diagonal strike 2.186 end strike to the power of 1.093 end exponent over denominator 2.187 end fraction middle dot 1 over up diagonal strike 2 to the power of 1 end cell row blank equals cell fraction numerator 1.093 over denominator 2.187 end fraction end cell end table end style

Jadi, jumlah begin mathsize 14px style 7 end style suku pertama deret geometri begin mathsize 14px style 1 third plus 1 over 9 plus 1 over 27 plus horizontal ellipsis end style sama dengan begin mathsize 14px style fraction numerator 1.093 over denominator 2.187 end fraction end style.

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