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Jika, 1 + 4 1 ​ + 9 1 ​ + 16 1 ​ + 25 1 ​ + ... = a , maka 9 1 ​ + 25 1 ​ + 49 1 ​ + ... = ...

Jika, , maka

  1. 1 fourth straight a minus 1

  2. 1 fourth straight a plus 1

  3. 3 over 4 straight a minus 1

  4. 3 over 4 straight a plus 1

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N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

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1 over 9 plus 1 over 25 plus 1 over 49 plus... equals 3 over 4 a minus 1

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Pembahasan

Jadi,

1 space plus space 1 fourth space plus space 1 over 9 space plus space 1 over 16 space plus space 1 over 25 space plus space.... space equals space straight a  tilde space space 1 space plus space 1 fourth space plus space 1 over 9 space plus space 1 over 16 space plus space 1 over 25 space plus space 1 over 36 space plus space 1 over 49 space plus space.... space equals space straight a  tilde space space 1 over 9 space plus space 1 over 25 space plus space 1 over 49 space plus space.... space equals space straight a space minus space 1 space minus space 1 fourth space minus space 1 over 16 space minus space 1 over 36  tilde space 1 over 9 space plus space 1 over 25 space plus space 1 over 49 space plus space.... space equals space straight a space minus space 1 space minus open parentheses 1 fourth space plus space 1 over 16 space plus space 1 over 36 space plus space... close parentheses  tilde space 1 over 9 space plus space 1 over 25 space plus space 1 over 49 space plus space.... space equals space straight a space minus space 1 space minus space 1 fourth space open parentheses space 1 space plus space 1 fourth space plus space 1 over 9 space plus space... close parentheses  tilde space 1 over 9 space plus space 1 over 25 space plus space 1 over 49 space plus space.... space equals space straight a space minus space 1 space minus space 1 fourth straight a  tilde space 1 over 9 space plus space 1 over 25 space plus space 1 over 49 space plus space.... space equals 3 over 4 straight a space minus space 1

Jadi, 1 over 9 plus 1 over 25 plus 1 over 49 plus... equals 3 over 4 a minus 1

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Diketahui barisan geometri 5,10, 20, 40, ... dan jumlah n suku pertamanya adalah 635. Tentukan banyak suku (n) dari deret tersebut.

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