Dark Mode

Recent questions tagged generating-functions

0 votes

0 answers

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

142 views

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

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

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

185 views

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

341 views

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

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

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

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

1.2k views

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

333 views

0 votes

1 answer

11

generating function

Rahul_Rathod_ asked in Combinatory Jan 15, 2019

by Rahul_Rathod_

414 views

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

325 views

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

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

Page:

1
2
3
4
next »

Recent questions tagged generating-functions