Pertanyaan

Jumlah deret tak hingga 3 1 x − 5 1 x 2 + 25 3 x 3 − 125 9 x 4 + . . . = 2 1 , apabila x sama dengan ....

Jumlah deret tak hingga

$\frac{1}{3} x - \frac{1}{5} x^{2} + \frac{3}{25} x^{3} - \frac{9}{125} x^{4} + . . . = \frac{1}{2}$ ,

apabila $x$ sama dengan ....

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Habis dalam

Klaim

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C

Pembahasan

Jadi, jawaban yang tepat adalah C

$begin mathsize 14px style S subscript infinity superscript g a n j i l end superscript plus S subscript infinity superscript g e n a p end superscript equals 1 half fraction numerator a over denominator 1 minus r squared end fraction plus fraction numerator a r over denominator 1 minus r squared end fraction equals 1 half fraction numerator begin display style 1 third end style x over denominator 1 minus open parentheses negative begin display style 3 over 5 end style x close parentheses squared end fraction plus fraction numerator begin display style 1 third end style x times open parentheses negative begin display style 3 over 5 end style x close parentheses over denominator 1 minus open parentheses negative begin display style 3 over 5 end style x close parentheses squared end fraction equals 1 half fraction numerator begin display style 1 third end style x minus begin display style 1 fifth end style x squared over denominator 1 minus begin display style 9 over 25 end style x squared end fraction equals 1 half 2 over 3 x minus 2 over 5 x squared equals 25 over 25 minus 9 over 25 x squared 9 over 25 x squared minus 2 over 5 x squared plus 2 over 3 x minus 25 over 25 equals 0 minus 1 over 25 x squared plus 2 over 3 x minus 25 over 25 equals 0 open parentheses negative 1 over 25 x squared plus 2 over 3 x minus 25 over 25 equals 0 close parentheses times open parentheses negative 75 close parentheses 3 x squared minus 50 x plus 75 equals 0 open parentheses 3 x minus 5 close parentheses open parentheses x minus 15 close parentheses equals 0 x equals 5 over 3 logical or x equals 15 end style$

Jadi, jawaban yang tepat adalah C