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GATE CSE 1987 | Question: 10b

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What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
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Fibonacci series :  1,1,2,3,5,8,13..........

Its generating function is :

1*z0 + 1*z1 +2*z2 +3*z3 +5*z4+-----------∞  =  G(z)

Above series can be rewritten as :

1 + (z +z2) + (z+z2)2 +....................∞  = G(z)

1/(1 - (z+z2)   = G(z)

Hence generating function G(z) =  1/(1- z -z2)

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