Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 6 Marks

Year: May 2016

1. {2,2,2,2 ----}

   Assume the generating function

   $f(x)=a_0+a_1x+a_2 x^2+a_3 x^3+……$

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

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

   Accordingly, $f(x) = 2(1-x)^{-1}$ is the generating function for the given sequence {2, 2, 2, 2, 2…………………}

2. {1,1,1,1---}

   Assume the generating function

   $f(x)=a_0+a_1x+a_2 x^2+a_3 x^3+……$

   But, the given sequence is {1, 1, 1, 1, 1…………………}. Using this sequence, the expression above becomes

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

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