Search results for generating-functions

0 votes
0 answers
22
4 votes
2 answers
23
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...
0 votes
1 answer
25
Is Exponential Generating Functions asked in GATE ?
1 votes
1 answer
27
27 votes
8 answers
29
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$$2^i$
1 votes
1 answer
30
Find the following sum.$$\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}$$1$
36 votes
8 answers
31
3 votes
1 answer
37
Find the generating function for the sequence $\left \{ a_n \right \} where $$a_n = \Large \binom{10}{n+1} $ for n = 0,1,2,….Sol. $\Large \binom{10}{1} + \binom{10}{2...
1 votes
3 answers
39
What will be solution of this function for coefficient of $x^{100}$?$$\frac{1}{\left ( 1-x^{10} \right )(1-x^{20})(1-x^{50})}$$
2 votes
2 answers
40