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Jumlah deret geometri tak hingga 5 + 4 15 + 16 45 + 64 135 + ..... adalah .....

Jumlah deret geometri tak hingga $5 + \frac{15}{4} + \frac{45}{16} + \frac{135}{64} + .....$ adalah .....

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R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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Pembahasan

Karena r <1 , jumlah deret tak hingga

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space Rasio left parenthesis straight r right parenthesis equals straight U subscript straight n over straight U subscript straight n minus 1 end subscript straight r equals fraction numerator begin display style 15 over 4 end style over denominator 5 straight r end fraction equals 3 over 4 straight U subscript 1 equals straight a equals 5$

Karena , jumlah deret tak hingga

$S subscript infinity equals fraction numerator a over denominator 1 minus r end fraction space space space space space space space equals fraction numerator 5 over denominator 1 minus begin display style 3 over 4 end style end fraction space space space space space space space space equals fraction numerator 5 over denominator begin display style 1 fourth end style end fraction space space space space space space space space equals 20$