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Diketahui jumlah deret geometri tak hingga adalah ...

Diketahui jumlah deret geometri tak hingga adalah begin mathsize 14px style 125 over 8 end style dan suku ke-2 adalah begin mathsize 14px style 5 over 2 end style. Rasio deret tersebut adalah ...

Jawaban:

begin mathsize 14px style u subscript n equals a. r to the power of n minus 1 end exponent u subscript 2 equals a. r equals 5 over 2 space space space space space space space space space space space a equals fraction numerator 5 over denominator 2 r end fraction s subscript infinity equals fraction numerator a over denominator 1 minus r end fraction equals 125 over 8 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 space space space space space space space space space space fraction numerator fraction numerator 5 over denominator 2 r end fraction over denominator 1 minus r end fraction equals 125 over 8 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 space space space space space space space space space space fraction numerator 40 over denominator 2 r end fraction equals 125 open parentheses 1 minus r close parentheses space space space space space space space space space space space space 20 over r equals 125 open parentheses 1 minus r close parentheses space space space space space space space space space space space space space space 20 equals 125 r minus 125 r squared 125 r squared minus 125 r plus 20 equals 0 space space space open parentheses 25 r minus 5 close parentheses open parentheses 5 r minus 4 close parentheses equals 0 r equals 1 fifth space atau space r equals 4 over 5 end style

Jadi, begin mathsize 14px style r equals 1 fifth space atau space r equals 4 over 5 end style 

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