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sauravshakya

  • 3 years ago

What is the n th term of the series: 1+1+2+3+5+8+13+21+...

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  1. Coolsector
    • 3 years ago
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    A(n) = A(n-1) + A(n-2) where a1 = 1 and a2 = 1 ?

  2. sauravshakya
    • 3 years ago
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    In terms of n

  3. estudier
    • 3 years ago
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    Looks familiar....

  4. Samkeyv
    • 3 years ago
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    N th term is given by the formulae A(n)=A(n+1)+A(n+2) N=(n+1)+(n+2)

  5. sauravshakya
    • 3 years ago
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    ???

  6. sauravshakya
    • 3 years ago
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    I know |dw:1350296451209:dw|

  7. sauravshakya
    • 3 years ago
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    But what in terms of n only.

  8. Coolsector
    • 3 years ago
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    it's funny that there is a question about the golden ratio now

  9. mukushla
    • 3 years ago
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    it is fibonacci...

  10. sauravshakya
    • 3 years ago
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    Yes

  11. kenttknguyen
    • 3 years ago
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    In terms of n ----> FIBOnnACCI

  12. mukushla
    • 3 years ago
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    \[F_n-F_{n-1}-F_{n-2}=0 \ \ \ n\ge2\] setting up characterestic equation gives\[\lambda^2-\lambda-1=0\]wchich gives\[\phi_1=\frac{1+\sqrt{5}}{2}\]\[\phi_2=\frac{1-\sqrt{5}}{2}\]and so\[F_n=A\phi_1^n+B\phi_2^n\]and all u need is finding A and B using the values of \(F_0\) and \(F_1\)

  13. mukushla
    • 3 years ago
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    finally

  14. sauravshakya
    • 3 years ago
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    @mukushla how |dw:1350297426979:dw|

  15. sauravshakya
    • 3 years ago
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    oh I get it now...... thanx

  16. Coolsector
    • 3 years ago
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    @sauravshakya may you explain how ?

  17. Coolsector
    • 3 years ago
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    i thought i got it but i realized that i was wrong

  18. Coolsector
    • 3 years ago
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    ok got it .. nvm :)

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