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+4 votes
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
asked in Combinatory by Veteran (39.7k points) 256 1308 1941
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2 Answers

+6 votes
Best answer
The general form is $G(x) = \frac{x}{1-x-x^2}$

and after solving this using partial fraction, we will get

$f_n=\frac{1}{\sqrt{5}}((\frac{1+\sqrt{5}}{2})^n- (\frac{1-\sqrt{5}}{2})^n)$
answered by Active (1.2k points) 6 17
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@manu madhavan, how did u get G(x)????
please explain sir
+1 vote
its solution is given in nptel discrete maths lecture no. 32 by kamala mam  (16:00 minutes)
answered by (367 points) 1 2 8

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