GATE Computer Science (CS) 2018 Shift 1 Solved Paper

Question : 15 of 65

Marks: +1, -0

Which one of the following is a closed form expression for the generating function of the sequence

\{a_{n}\}

, where

a_{n}=2 n+3

for all

n=0,1,2, . . . . . ?

Solution:

The Given functions is,

a_{n}=2 n+3

generating function for 1 is

\;{1}/{1-x}

and

n

\;{x}/{(1-x)^{2}}

, the generating function for

a_{n}

A(x)=\;{2 x}/{(1-x)^{2}}+\;{3}/{1-x}

=\;{2 x+3(1-x)}/{(1-x)^{2}}=\;{3-x}/{(1-x)^{2}}

Which is option (d).

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