Question

Find the generating function for the sequence 0^2 , 1^2 , 2^2 , 3^2 ..

Answer 1

Answer:

Give a numerical : sequence the series is called the generating function of the sequence

Answer 2

Answer:

Concept:

Generating function is a way of encoding an infinite sequence of numbers by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence.

Given:

$0^{2},1^{2}, 2^{2}, 3^{2} ....$

To Find:

The generating function of given sequence

Explanation:

the sequence is $0^{2},1^{2}, 2^{2}, 3^{2} ....$ that is $n^{2}$

∴ its generating function is$\frac{z(1+z) }{(1-z)^{3} }$