Q7Discrete Mathematics Structure

Question

What is a generating function? Give example.

Answer 1

A generating function for a sequence $a_{0}, a_{1}, a_{2}, \dots$ is an infinite series of the form $G (x) = \sum_{n = 0}^{\infty} a_{n} x^{n} = a_{0} + a_{1} x + a_{2} x^{2} + \dots$ .

Example: For the sequence $1, 1, 1, \dots$ the generating function is $G (x) = 1 + x + x^{2} + \dots = \frac{1}{1 - x}$ for $∣ x ∣ < 1$ .

Q7Discrete Mathematics Structure

Question

Answer