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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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