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Find the generating function for the following sequence

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 4 Marks

Year: Dec 2014

1 Answer
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  1. 3, 3, 3, 3, 3………………

    Assume the generating function

    $f(x)=a_0+a_1x+a_2 x^2+a_3 x^3+……$

    But, the given sequence is {2. 3, 3, 3, 3, 3…………………}. Using this sequence, the expression above becomes

    f(x)$=3 +3x+3x^2+3x^3+……\\ =3(1+x+x^2+x^3+…….)\\ =3(1-x)^{-1}$

    Accordingly, $f(x) = 3(1-x)^{-1}$ is the generating function for the given sequence {3, 3, 3, 3, 3…………………}

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