Lecture 8

Learning objectives

After this class, you should be able to:

1. Derive formulas for the basic operations that can be performed on generating functions.
2. Give generating functions and their closed form expressions for some common sequences.
3. Given a sequence, use the basic operations on generating functions to determine a closed form expression for the generating function.

Reading assignment

1. Sec 7.2.

Exercises and review questions

• Questions on current lecture's material
  1. Derive the generating function and its closed form expression for each of the following sequences: (a) < 1, 1/2, 1/3, 1/4, ... > , (b) < 0, 0, 1, 1/2, 1/3, 1/4, ... >, (c) < 0, 0, -1, 1/2, -1/3, 1/4, ... >, (d) < 0*1, 1*2, 2*4, 3*8, 4*16, ... >, (e) < 1/1, 2/2, 4/3, 8/4, ... >.
  2. Prove the 13th formula in table 335.

• Questions on next lecture's material
  1. None.