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Recent questions tagged generating-functions

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Generating Functions
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GO Classes 2023 | IIITH Mock Test 1 | Question: 33
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ where $a_n = \binom {n+4}{n}$ for $n= 0,1,2,\ldots ?$\frac{1}{(1-x)^5}$\frac{5}{(1-x)}$\frac{1}{(1-x)^4}$\frac{x}{(1-x)^5}$
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kenneth h rosen chapter 6
What is the closed form for the generating function for the sequence : 0,1,-2,4,-8,16,-32,64,...
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DRDO CSE 2022 Paper 1 | Question: 15
What is the generating function corresponding to Fibonacci series.\[F_{n}=F_{n-1}+F_{n-2} .\]Note that $F_{0}=F_{1}=1$.
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DRDO CSE 2022 Paper 1 | Question: 16
Let us say we have a supply of $1$ rupee and $2$ rupee coins in large quantities. What is the generating function for the number of ways of giving change with $1$ rupee and $2$ rupee coins.
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Engineering Mathematics
How the value of a1 = 3, a2 = 2 is calculated.
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GO Classes Scholarship 2023 | Test | Question: 7
Define the generating functions $\text{B}(x)=\displaystyle{} \sum_{n=0}^{\infty} 2^{n} x^{n}$ and $F(x)=\displaystyle{} \sum_{n=0}^{\infty} f_{n} x^{n}$ ... $x^{5}$ is $\mathrm{G}(x)?$
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GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ ... \frac{1}{1-x}$\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$
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TIFR CSE 2021 | Part A | Question: 11
Find the following sum.$\frac{1}{2^{2}-1}+\frac{1}{4^{2}-1}+\frac{1}{6^{2}-1}+\cdots+\frac{1}{40^{2}-1}$$\frac{20}{41}$\frac{10}{41}$\frac{10}{21}$\frac{20}{21}$1$
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