Generating Functions: Examples - Part 1

In this video, we present a number of examples of sequence Generating Functions and their construction from the underlying sequence. In particular, we construct the generating functions for the sequences:

A) [2, 4, 6, 8, 10, ...]
B) [0, 0, 0, 2, 4, 6, 8, ...]
C) [1, 5, 25, 125, ...]
D) [1, -3, 9, -27, 81, ...]
E) [1, 0, 5, 0, 25, 0, 125, 0, ...]
F) [0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, ...]

The techniques presented are dependent on the properties associated with substitution into and multiplication of the constant sequence [1, 1, 1, 1, ...] as well as others.