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Recent questions tagged generating-functions

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3
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,...
What is the closed form for the generating function for the sequence : 0,1,-2,4,-8,16,-32,64,...
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1 votes
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4
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 $F_{0}=F_{1}=1$.
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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5
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.
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 a...
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6
Engineering Mathematics
How the value of a1 = 3, a2 = 2 is calculated.
How the value of a1 = 3, a2 = 2 is calculated.
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9
TIFR CSE 2021 | Part A | Question: 11
Find the following sum. $\frac{1}{2^{2}-1}+\frac{1}{4^{2}-1}+\frac{1}{6^{2}-1}+\cdots+\frac{1}{40^{2}-1}$ $\frac{20}{41}$ $\frac{10}{41}$ $\frac{10}{21}$ $\frac{20}{21}$ $1$
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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3 votes
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11
GATE Overflow Test Series | Mock GATE | Test 4 | Question: 13
If an ordinary generating function sequence is $\{a_n\}_{0}^{\infty} = \frac{x}{(1-3x)^2}$. Then $a_4 - a_1$ is equal to _________
If an ordinary generating function sequence is $\{a_n\}_{0}^{\infty} = \frac{x}{(1-3x)^2}$. Then $a_4 - a_1$ is equal to _________
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21 votes
2 answers
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GATE Overflow Test Series | Mock GATE | Test 2 | Question: 28
The generating function for the sequence with recurrence relation $a_n=3a_{n-1}-a_{n-2}$ with initial terms $a_0=1$ and $a_1=5$ is. $\frac{1+2x}{1-3x+x^2}$ $\frac{1-2x}{1-3x+x^2}$ $\frac{1+2x}{1+3x+x^2}$ $\frac{1+x}{1-3x+x^2}$
The generating function for the sequence with recurrence relation $a_n=3a_{n-1}-a_{n-2}$ with initial terms $a_0=1$ and $a_1=5$ is.$\frac{1+2x}{1-3x+x^2}$$\frac{1-2x}{1-3...
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GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 16
The generating function corresponding to $4,5,7,10,14,19,25,\dots $ is ? $\frac{4}{1-x} + \frac{x}{(1-x)^3}$ $\frac{2}{1-x} + \frac{x}{(1-x)^3}$ $\frac{4}{1-x} + \frac{x}{(1-x)^2}$ $\frac{x}{(1-x)^3}$
The generating function corresponding to $4,5,7,10,14,19,25,\dots $ is ?$\frac{4}{1-x} + \frac{x}{(1-x)^3}$$\frac{2}{1-x} + \frac{x}{(1-x)^3}$$\frac{4}{1-x} + \frac{x}{(1...
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3 votes
1 answer
18
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 14
Match the sequences on the left with their corresponding generating functions on the right ... $A-P,B-Q,C-R,D-S$ $A-P,B-R,C-S,D-Q$ $A-Q,B-R,C-S,D-P$ None of the above
Match the sequences on the left with their corresponding generating functions on the right$$\begin{array}{|cl|cl|} \hline A. & 0,1,2,3,4,5,6,7,\ldots & P. & \frac{x(1+x)}...
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5 votes
2 answers
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GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 23
Which of the following is the generating function corresponding to the sequence $0,1,0,0,2,0,0,3,0,0,4,0,0,5, \dots $. $\frac{x^3}{(1-x)}$ $\frac{x}{(1-x)^2}$ $\frac{x}{(1-x^3)^2}$ $\frac{x}{1-x^3}$
Which of the following is the generating function corresponding to the sequence $0,1,0,0,2,0,0,3,0,0,4,0,0,5, \dots $.$\frac{x^3}{(1-x)}$$\frac{x}{(1-x)^2}$$\frac{x}{(1-x...
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