anonymous
  • anonymous
What is the n th term of the series: 1+1+2+3+5+8+13+21+...
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
A(n) = A(n-1) + A(n-2) where a1 = 1 and a2 = 1 ?
anonymous
  • anonymous
In terms of n
anonymous
  • anonymous
Looks familiar....

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anonymous
  • anonymous
N th term is given by the formulae A(n)=A(n+1)+A(n+2) N=(n+1)+(n+2)
anonymous
  • anonymous
???
anonymous
  • anonymous
I know |dw:1350296451209:dw|
anonymous
  • anonymous
But what in terms of n only.
anonymous
  • anonymous
it's funny that there is a question about the golden ratio now
anonymous
  • anonymous
it is fibonacci...
anonymous
  • anonymous
Yes
anonymous
  • anonymous
In terms of n ----> FIBOnnACCI
anonymous
  • anonymous
\[F_n-F_{n-1}-F_{n-2}=0 \ \ \ n\ge2\] 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 \(F_1\)
anonymous
  • anonymous
anonymous
  • anonymous
@mukushla how |dw:1350297426979:dw|
anonymous
  • anonymous
oh I get it now...... thanx
anonymous
  • anonymous
@sauravshakya may you explain how ?
anonymous
  • anonymous
i thought i got it but i realized that i was wrong
anonymous
  • anonymous
ok got it .. nvm :)

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