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