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Recent questions tagged generating-functions
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1
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,...
Shivam_j
asked
in
Combinatory
Dec 23, 2022
by
Shivam_j
142
views
generating-functions
1
vote
1
answer
2
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 $F_{0}=F_{1}=1$.
admin
asked
in
Combinatory
Dec 15, 2022
by
admin
129
views
drdocse-2022-paper1
combinatory
generating-functions
6-marks
descriptive
1
vote
0
answers
3
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.
admin
asked
in
Combinatory
Dec 15, 2022
by
admin
61
views
drdocse-2022-paper1
combinatory
generating-functions
5-marks
descriptive
0
votes
0
answers
4
Engineering Mathematics
How the value of a1 = 3, a2 = 2 is calculated.
Overflow04
asked
in
Mathematical Logic
Aug 25, 2022
by
Overflow04
185
views
engineering-mathematics
generating-functions
test-series
3
votes
1
answer
5
GO Classes Scholarship 2023 | Test | Question: 7
Define the generating functions $\text{B}(x)=\displaystyle{} \sum_{n=0}^{\infty} 2^{n} x^{n}$ and $F(x)=\displaystyle{} \sum_{n=0}^{\infty} f_{n} x^{n}$ where $f_{n}$ ... $x^{5}$ is $\mathrm{G}(x)?$
GO Classes
asked
in
Combinatory
Aug 7, 2022
by
GO Classes
341
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
generating-functions
2-marks
20
votes
5
answers
6
GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$
Arjun
asked
in
Combinatory
Feb 15, 2022
by
Arjun
4.1k
views
gatecse-2022
combinatory
generating-functions
2-marks
1
vote
1
answer
7
TIFR CSE 2021 | Part A | Question: 11
Find the following sum. $\frac{1}{2^{2}-1}+\frac{1}{4^{2}-1}+\frac{1}{6^{2}-1}+\cdots+\frac{1}{40^{2}-1}$ $\frac{20}{41}$ $\frac{10}{41}$ $\frac{10}{21}$ $\frac{20}{21}$ $1$
soujanyareddy13
asked
in
Combinatory
Mar 25, 2021
by
soujanyareddy13
361
views
tifr2021
combinatory
generating-functions
4
votes
1
answer
8
ISI2018-MMA-26
Let $C_i(i=0,1,2...n)$ be the coefficient of $x^i$ in $(1+x)^n$.Then $\frac{C_0}{2} – \frac{C_1}{3}+\frac{C_2}{4}-\dots +(-1)^n \frac{C_n}{n+2}$ is equal to $\frac{1}{n+1}\\$ $\frac{1}{n+2}\\$ $\frac{1}{n(n+1)}\\$ $\frac{1}{(n+1)(n+2)}$
akash.dinkar12
asked
in
Combinatory
May 11, 2019
by
akash.dinkar12
1.4k
views
isi2018-mma
engineering-mathematics
discrete-mathematics
generating-functions
1
vote
3
answers
9
ACE Test Series: Generating Function
The generating function of the sequence $\left \{ a_{0},a_{1},a_{2}..........a_{n}………...\infty \right \}$ where $a_{n}=\left ( n+2 \right )\left ( n+1 \right ).3^{n}$ is $a)3\left ( 1+3x \right )^{-2}$ $b)3\left ( 1-3x \right )^{-2}$ $c)2\left ( 1+3x \right )^{-3}$ $d)2\left ( 1-3x \right )^{-3}$
srestha
asked
in
Combinatory
Mar 8, 2019
by
srestha
1.2k
views
generating-functions
discrete-mathematics
3
votes
1
answer
10
Rosen 7e, Advance Counting techniques , Question 6.f
Find the generating function for the sequence $\left \{ a_n \right \} where $ $a_n = \Large \binom{10}{n+1} $ ... $\Large \color{red}{ \frac{( 1+x )^{10} - 1}{x} }$ Please verify
Mk Utkarsh
asked
in
Combinatory
Mar 7, 2019
by
Mk Utkarsh
333
views
kenneth-rosen
discrete-mathematics
generating-functions
0
votes
1
answer
11
generating function
Rahul_Rathod_
asked
in
Combinatory
Jan 15, 2019
by
Rahul_Rathod_
414
views
generating-functions
discrete-mathematics
combinatory
discrete
1
vote
0
answers
12
MadeEasy Full Length Test 2019: Combinatory - Generating Functions
Let We define Then ar is equal to. $\binom{r}{2019}$ $\binom{r}{r + 2018}$ $\binom{r}{2019 - r}$ $\binom{r}{r - 2018}$ Can anyone tell me if this type of question is in Gate 2019 syllabus or ... question in previous year question? If yes, then when can I learn this stuff from. Because I am unable to understand the whole solution.
jhaanuj2108
asked
in
Combinatory
Jan 13, 2019
by
jhaanuj2108
325
views
discrete-mathematics
generating-functions
made-easy-test-series
1
vote
0
answers
13
Kenneth Rosen Edition 6th Exercise 7.4 Question 7,8 (Page No. 496)
For each of these generating functions, provide a closed formula for the sequence it determines. $a) (3x − 4)^{3}$ $b) (x^{3} + 1)^{3}$
Sandy Sharma
asked
in
Mathematical Logic
Dec 29, 2018
by
Sandy Sharma
730
views
discrete-mathematics
kenneth-rosen
generating-functions
2
votes
1
answer
14
GATE Overflow | Mock GATE | Test 1 | Question: 11
Which one of the following best expresses the generating function sequence $\{a_n\}$, for the given closed form representation? $F(x) = \frac{1}{1-x-x^2}$ $a_n=a_{n-1}+3, n>0, a_0=1$ $a_n=a_{n-1}+a_{n-2}, n>1, a_0=1, a_1=1$ $a_n=2n+3, n>1$ $a_n=2a_{n-1}+3, n>1, a_0=1$
Ruturaj Mohanty
asked
in
Set Theory & Algebra
Dec 27, 2018
by
Ruturaj Mohanty
928
views
go-mockgate-1
combinatory
generating-functions
set-theory&algebra
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