Exercise 2.
Find the sequence generated by the following generating functions:
\(\dfrac{4x}{1-x}\text{.}\)
\(\dfrac{1}{1-4x}\text{.}\)
\(\dfrac{x}{1+x}\text{.}\)
\(\dfrac{3x}{(1+x)^2}\text{.}\)
\(\dfrac{1+x+x^2}{(1-x)^2}\) (Hint: multiplication).
Find the sequence generated by the following generating functions:
\(\dfrac{4x}{1-x}\text{.}\)
\(\dfrac{1}{1-4x}\text{.}\)
\(\dfrac{x}{1+x}\text{.}\)
\(\dfrac{3x}{(1+x)^2}\text{.}\)
\(\dfrac{1+x+x^2}{(1-x)^2}\) (Hint: multiplication).