Lecture 18

Learning objectives

After this class, you should be able to:

1. Prove the theorem on page 341.
2. Apply the above theorem to express a rational function as partial fractions, and to solve a recurrence using generating functions.

Reading assignment

1. Page 341-342.

Exercises and review questions

• Questions on current lecture's material
  1. Express the following fraction as partial fractions: z/((1-z)2 (1+2z)2).
  2. Express the following fraction as partial fractions: (3z+1)/((1+z) (1-z)2 (1+2z)3).

• Questions on next lecture's material
  1. Equation 7.31 on page 341 gives two expression for ak. Show that they are identical. (You need not show that they are the correct expressions for ak; it is sufficient to show that they are equal.)