Question

2.1. Find the ordinary generating functions for the following sequences. (a) (1, 1, 1, 1, 0, 0, ...} (b) (0, 0, 0, 0, 1, 1, ...) (c) {1, 1, 1, 1,...} (d) (1,-1, 1,-1,...}

Answer 1

(a)   

1+x+x +x

(b)
+ + x + 6 + ....
=
x+(1+1+2 + ...)
=   $\frac{x^{4}}{1-x}$

(c)   
1+C+ + + ++..
= $\frac{1}{1-x}$

(d)
1 - 2 + 1 - 2 + x + - ....
=  $\frac{1}{1+x}$

// If you have any doubts, please mention in the comment section.

// If you got the answer, please upvote :)