Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ , where $a_n = 2n + 3$ for all $n = 0, 1, 2, \dots$ ?

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Combinatorics

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How GATE tests Combinatorics

GATE evaluates Generating Functions by testing the candidate's ability to find closed-form representations of ordinary generating functions (OGFs) for piecewise or parity-dependent sequences. Questions require decomposing sequences linearly and applying operations like substitution (e.g., x2) and differentiation to handle polynomial coefficients. These items test analytical fluency with infinite series and discrete mathematics manipulations.

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GATE CSE 2018 Q1 · MCQ · 1 mark

Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ , where $a_n = 2n + 3$ for all $n = 0, 1, 2, \dots$ ?

Select an option to check

Key concept

Combinatorics

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Combinatorics

Full Combinatorics guide →

More on Combinatorics

All 19 questions on Combinatorics →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ , where $a_n = 2n + 3$ for all $n = 0, 1, 2, \dots$ ?

Step-by-step verified solution

Check you can still solve Combinatorics under a clock

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Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ , where $a_n = 2n + 3$ for all $n = 0, 1, 2, \dots$ ?

Step-by-step verified solution

Check you can still solve Combinatorics under a clock

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Which one of the following is a closed form expression for the generating function of the sequence {an}\{a_n\}{an​}, where an=2n+3a_n = 2n + 3an​=2n+3 for all n=0,1,2,…n = 0, 1, 2, \dotsn=0,1,2,… ?

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Check you can still solve Combinatorics under a clock

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Which one of the following is a closed form expression for the generating function of the sequence {an}\{a_n\}{an​}, where an=2n+3a_n = 2n + 3an​=2n+3 for all n=0,1,2,…n = 0, 1, 2, \dotsn=0,1,2,… ?

Step-by-step verified solution

Check you can still solve Combinatorics under a clock

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Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ , where $a_n = 2n + 3$ for all $n = 0, 1, 2, \dots$ ?

Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ , where $a_n = 2n + 3$ for all $n = 0, 1, 2, \dots$ ?