sauravshakya
What is the n th term of the series:
1+1+2+3+5+8+13+21+...
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Coolsector
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A(n) = A(n-1) + A(n-2)
where a1 = 1 and a2 = 1
?
sauravshakya
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In terms of n
estudier
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Looks familiar....
Samkeyv
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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)
sauravshakya
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???
sauravshakya
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I know |dw:1350296451209:dw|
sauravshakya
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But what in terms of n only.
Coolsector
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it's funny that there is a question about the golden ratio now
mukushla
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it is fibonacci...
sauravshakya
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Yes
kenttknguyen
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In terms of n ----> FIBOnnACCI
mukushla
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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 \(F_1\)
mukushla
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finally
sauravshakya
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@mukushla how |dw:1350297426979:dw|
sauravshakya
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oh I get it now...... thanx
Coolsector
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@sauravshakya may you explain how ?
Coolsector
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i thought i got it but i realized that i was wrong
Coolsector
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ok got it .. nvm :)