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Search results for generating-functions
3
votes
1
answer
21
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 $\mathrm{G}(x)?$
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 $f_{n}$ is ...
GO Classes
631
views
GO Classes
asked
Aug 6, 2022
Combinatory
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
generating-functions
2-marks
+
–
0
votes
0
answers
22
Engineering Mathematics
How the value of a1 = 3, a2 = 2 is calculated.
How the value of a1 = 3, a2 = 2 is calculated.
Overflow04
449
views
Overflow04
asked
Aug 25, 2022
Mathematical Logic
engineering-mathematics
generating-functions
test-series
+
–
4
votes
2
answers
23
Generating function
Find $\large\color{maroon}{a^n}$ for the following generating function, $\color{green}{\begin{align*} \frac{1}{1-2x^2} \end{align*}}$ $\large\color{maroon}{a^n}$ = closed form of the $nth$ term in the corresponding sequence.
Find $\large\color{maroon}{a^n}$ for the following generating function,$$\color{green}{\begin{align*} \frac{1}{1-2x^2} \end{align*}}$$$\large\color{maroon}{a^n}$ = closed...
dd
1.9k
views
dd
asked
Dec 21, 2016
Combinatory
generating-functions
combinatory
+
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0
votes
1
answer
24
General Doubt on Generating Functions
Given only a Generating Function in closed form can we find the sequence it represents? If so, how? Please explain with an example.If not, given a GF(closed form) in general what information does it convey to us about a series if the series is not provided ?
Given only a Generating Function in closed form can we find the sequence it represents? If so, how? Please explain with an example.If not, given a GF(closed form) in gen...
tonystark
371
views
tonystark
asked
Oct 16, 2018
Combinatory
generating-functions
discrete-mathematics
kenneth-rosen
combinatory
counting
+
–
0
votes
1
answer
25
Exponential Generating Function
Is Exponential Generating Functions asked in GATE ?
Is Exponential Generating Functions asked in GATE ?
Na462
364
views
Na462
asked
Apr 30, 2018
Mathematical Logic
generating-functions
+
–
0
votes
1
answer
26
Kenneth Rosen Edition 6th Exercise 6.4 Question 47 (Page No. 442)
rahul sharma 5
816
views
rahul sharma 5
asked
Jun 18, 2017
Mathematical Logic
combinatory
discrete-mathematics
kenneth-rosen
generating-functions
+
–
1
votes
1
answer
27
binomial coefficient
Aditya Bahuguna
653
views
Aditya Bahuguna
asked
Jan 5, 2018
Combinatory
generating-functions
+
–
2
votes
2
answers
28
Ace Test series: Combinatory - Generating Functions
Answer is B as given in solution.
Answer is B as given in solution.
ashish pal
538
views
ashish pal
asked
Jan 6, 2018
Combinatory
ace-test-series
discrete-mathematics
generating-functions
+
–
27
votes
8
answers
29
GATE CSE 2005 | Question: 50
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$?$i$$i+1$$2i$$2^i$
gatecse
8.1k
views
gatecse
asked
Sep 21, 2014
Combinatory
gatecse-2005
normal
generating-functions
+
–
1
votes
1
answer
30
TIFR CSE 2021 | Part A | Question: 11
Find the following sum. $\frac{1}{2^{2}-1}+\frac{1}{4^{2}-1}+\frac{1}{6^{2}-1}+\cdots+\frac{1}{40^{2}-1}$ $\frac{20}{41}$ $\frac{10}{41}$ $\frac{10}{21}$ $\frac{20}{21}$ $1$
Find the following sum.$$\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}$$1$
soujanyareddy13
631
views
soujanyareddy13
asked
Mar 25, 2021
Combinatory
tifr2021
combinatory
generating-functions
+
–
36
votes
8
answers
31
GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
makhdoom ghaya
9.7k
views
makhdoom ghaya
asked
Nov 14, 2016
Combinatory
gate1987
combinatory
generating-functions
descriptive
+
–
29
votes
7
answers
32
TIFR CSE 2010 | Part A | Question: 12
The coefficient of $x^{3}$ in the expansion of $(1 + x)^{3} (2 + x^{2})^{10}$ is. $2^{14}$ $31$ $\left ( \frac{3}{3} \right ) + \left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) + 2\left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) \left ( \frac{10}{1} \right ) 2^{9}$
The coefficient of $x^{3}$ in the expansion of $(1 + x)^{3} (2 + x^{2})^{10}$ is.$2^{14}$$31$$\left ( \frac{3}{3} \right ) + \left ( \frac{10}{1} \right )$$\left ( \frac{...
makhdoom ghaya
3.2k
views
makhdoom ghaya
asked
Oct 3, 2015
Combinatory
tifr2010
generating-functions
+
–
2
votes
1
answer
33
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? $F(x) = \frac{1}{1-x-x^2}$ $a_n=a_{n-1}+3, n>0, a_0=1$ $a_n=a_{n-1}+a_{n-2}, n>1, a_0=1, a_1=1$ $a_n=2n+3, n>1$ $a_n=2a_{n-1}+3, n>1, a_0=1$
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,...
Ruturaj Mohanty
1.3k
views
Ruturaj Mohanty
asked
Dec 27, 2018
Set Theory & Algebra
go-mockgate-1
combinatory
generating-functions
set-theory&algebra
+
–
3
votes
1
answer
34
Kenneth Rosen Edition 6th Exercise 6.4 Question 13 (Page No. 440)
Use Generating function to determine,the number of different ways $10$ identical balloons can be given to four children if each child receives atleast $2$ ballons? Ans given $(x^{2}+x^{3}+.........................)^{4}$ But as there is a upper ... Which one is correct? plz confirm
Use Generating function to determine,the number of different ways $10$ identical balloons can be given to four children if each child receives atleast $2$ ballons?Ans giv...
srestha
2.0k
views
srestha
asked
Dec 4, 2018
Combinatory
kenneth-rosen
discrete-mathematics
generating-functions
+
–
6
votes
1
answer
35
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 $\frac{1}{n+1}\\$ $\frac{1}{n+2}\\$ $\frac{1}{n(n+1)}\\$ $\frac{1}{(n+1)(n+2)}$
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+...
akash.dinkar12
1.8k
views
akash.dinkar12
asked
May 11, 2019
Combinatory
isi2018-mma
engineering-mathematics
discrete-mathematics
generating-functions
+
–
1
votes
1
answer
36
Kenneth Rosen Edition 6th Exercise 6.4 Question 39 (Page No. 442)
What is the generating function for the sequence of Fibonacci numbers?
What is the generating function for the sequence of Fibonacci numbers?
air1ankit
380
views
air1ankit
asked
Oct 9, 2017
Combinatory
combinatory
propositional-logic
kenneth-rosen
discrete-mathematics
generating-functions
+
–
3
votes
1
answer
37
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
Find the generating function for the sequence $\left \{ a_n \right \} where $$a_n = \Large \binom{10}{n+1} $ for n = 0,1,2,….Sol. $\Large \binom{10}{1} + \binom{10}{2...
Mk Utkarsh
520
views
Mk Utkarsh
asked
Mar 7, 2019
Combinatory
kenneth-rosen
discrete-mathematics
generating-functions
+
–
7
votes
2
answers
38
MadeEasy Test Series 2019: Combinatory- Generating Functions
Let $M(x) = \frac{x^{2018}}{(1-x)^{2019}}$ we define $M(x) = \sum_{r=0}^{\infty}a_{r}x^{r}$ ,then $a_{r}$ is equal to- $A)\binom{r}{2019}$ $B)\binom{r}{r+2018}$ $C)\binom{r}{2019-r}$ $D)\binom{r}{r-2018}$
Let $M(x) = \frac{x^{2018}}{(1-x)^{2019}}$we define $M(x) = \sum_{r=0}^{\infty}a_{r}x^{r}$ ,then $a_{r}$ is equal to-$A)\binom{r}{2019}$$B)\binom{r}{r+2018}$$C)\binom{r}{...
register_user_19
950
views
register_user_19
asked
Dec 15, 2018
Combinatory
discrete-mathematics
generating-functions
made-easy-test-series
+
–
1
votes
3
answers
39
Generating Function
What will be solution of this function for coefficient of $x^{100}$? $\frac{1}{\left ( 1-x^{10} \right )(1-x^{20})(1-x^{50})}$
What will be solution of this function for coefficient of $x^{100}$?$$\frac{1}{\left ( 1-x^{10} \right )(1-x^{20})(1-x^{50})}$$
srestha
1.7k
views
srestha
asked
Dec 3, 2018
Combinatory
generating-functions
discrete-mathematics
+
–
2
votes
2
answers
40
Rolling of a dice
The number of ways to roll 5 six sided dice to get sum of 25 is ________. _________________________________________________________ if solving with generating function, then why dividing by $\left ( 1-x \right )$ if equation is $\frac{x\left ( 1-x^{6} \right )}{\left ( 1-x \right )}$?
The number of ways to roll 5 six sided dice to get sum of 25 is ________._________________________________________________________if solving with generating function, the...
srestha
2.0k
views
srestha
asked
Aug 23, 2018
Combinatory
generating-functions
+
–
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