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shubhamsrg

  • 3 years ago

Let a_n = 1.............1 with 3^n digits. Prove that a_n is divisible by 3a_(n-1).

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  1. shubhamsrg
    • 3 years ago
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    |dw:1345625544093:dw|

  2. nightwill
    • 3 years ago
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    a_n = 1...11...11..1 (divided them into three parts) a_(n-1)= 1...1 a_n/a_(n-1)=10...010...01 Example n=2 a_n=111 111 111 a_(n-1)=111 a_n/a_(n-1) = 1 001 001 n=3 a_n= 111111111 111111111 111111111 a_(n-1) = 111111111 a_n/a_(n-1) = 1 000000001 000000001

  3. shubhamsrg
    • 3 years ago
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    hmms,,seems satisfactory,,thanks! :)

  4. shubhamsrg
    • 3 years ago
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    can we use induction here? just to generalize things more?

  5. shubhamsrg
    • 3 years ago
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    bah,,let it be,,thanks again..

  6. nightwill
    • 3 years ago
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    You're welcome ^^

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