GATE | GATE CS 2018 | Question 18
Which one the following is a closed form expression for the generating function of the sequence {an}, where an = 2n + 3 for all n = 0, 1, 2,…?
(A) A
(B) B
(C) C
(D) D
Answer: (D)
Explanation: Given an = 2n + 3
Generating function G(x) for the sequence an is
G(x) = 
= 
= 
= 2(0+x+2x2+3x3+…..) + 3(1+x+x2+….)
We know that 
= 1+x+x2+….
x+2x2+3x3+… = x(1+2x+3x2+….) = 
Substituting calculated values in G(x)
G(x) = 
= 
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