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AravindG

  • 3 years ago

guys anyone knows mathematical induction?

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  1. DHASHNI
    • 3 years ago
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    yep

  2. nilankshi
    • 3 years ago
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    sorry , i don't know

  3. AravindG
    • 3 years ago
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    i hav a question can u help?

  4. konfab
    • 3 years ago
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    fire away

  5. DHASHNI
    • 3 years ago
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    ya sure so on writing ur question!!1

  6. AravindG
    • 3 years ago
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    n-3^(2n+2)-8n-9 is divisible by 8.Prove

  7. DHASHNI
    • 3 years ago
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    is ur question correct!!!!1

  8. AravindG
    • 3 years ago
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    no srry

  9. AravindG
    • 3 years ago
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    3^(2n+2)-8n-9 is divisible by 8.Prove

  10. AravindG
    • 3 years ago
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    ............

  11. AravindG
    • 3 years ago
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    ???

  12. DHASHNI
    • 3 years ago
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    let p(n)=n-3^(2n+2)-8n-9 =8m (let m be any value) checking for p(1), lhs: p(1)= 3^(2+2) -8-9=81-17=64=8x8=8m =rhs therefore p(1)is true assume p(k)is true . =>3^(2k+2)-8k-9=8m \[=>3^{(2k)} = \frac{8m+8k+9}{3^{2}}\]-----(1) to prove :p(k+1)is true substitute k+1 in n in the given eq \[=>3^{2k+4}-8(k+1)-9= 3^{2k}.3^{4}-8k-17\]substitute (1) instead of 3^(2k) =>72m+64k+64= =>8(9m+8k+8) therefore p(k+1) is true by principal of mathematical induction , p(n) is true for all n belonging to natural numbers

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