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Jumlah suatu deret geometri tak hingga yang konvergen adalah 64 dan jumlah dua suku pertamanya adalah 39. Rasio deret tersebut jika rasionya positif adalah ....

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$S infinity equals fraction numerator a over denominator 1 minus r end fraction 64 equals fraction numerator a over denominator 1 minus r end fraction left right double arrow 64 left parenthesis 1 minus r right parenthesis equals a.... left parenthesis i right parenthesis S subscript 2 equals fraction numerator a left parenthesis 1 minus r right parenthesis squared over denominator 1 minus r end fraction 39 equals fraction numerator a left parenthesis 1 minus r right parenthesis squared over denominator 1 minus r end fraction... left parenthesis i i right parenthesis S u b s t i t u s i k a n space p e r s a m a a n space left parenthesis i right parenthesis space k e space p e r s a m a a n space left parenthesis i i right parenthesis colon 39 equals fraction numerator 64 up diagonal strike left parenthesis 1 minus r right parenthesis end strike left parenthesis 1 minus r squared right parenthesis over denominator up diagonal strike left parenthesis 1 minus r right parenthesis end strike end fraction 39 equals 64 minus 64 r squared 64 r squared equals 25 r squared equals 25 over 64 left right double arrow r square root of 25 over 64 end root left right double arrow r equals plus-or-minus 5 over 8 K a r e n a space r space p o s i t i f comma space m a k a space r equals 5 over 8$