I was just working on proving the Fibonacci sequence and the Golden ratio i think, but i was having one problem.(adsbygoogle = window.adsbygoogle || []).push({});

I was asked to prove that An=Bn, where An+2=An+1 + An (the fibonacci sequence) and that Bn=1/root5 [(1+root5/2)^n - (1 - root5/2)^n].

I understood the whole problem and was half way in completing until i wasn't able to go any further. Knowin that the limit existed i came up with

L=[1+/- root 5 ]/2

then i was told that C+D=1 and C(L)+D(-L)=1, and by solving for C and D by these two equations, i would get

Bn=1/root5 [(1+root5/2)^n - (1 - root5/2)^n].

But the values of C and D cancel out or i m getting like a zero for one of them. What did i do wrong, and what am i suppose to do next?

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# Homework Help: Fibonacci sequence

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