19.1. Discrete Mathematics

Try these first

1. 1.

   What does F(n) represent in a linear non-homogeneous recurrence equation?

   Hint

   Think about its role in the equation.

2. 2.

   How do we derive the associated homogeneous relation?

   Hint

   What do we need to focus on when we remove F(n)?

3. 3.

   What characterizes a non-homogeneous recurrence equation?

   • Only previous terms
   • Previous terms and a function of n
   • Only constants

   Hint

   Focus on the additional term's role.

4. 4.

   True or False: The associated homogeneous relation is derived by adding F(n).

   • True
   • False

   Hint

   What happens to F(n) in the homogeneous equation?

5. 5.

   Solve the recurrence relation a(n) = 2a(n-1) + 3n with a(0) = 0.

   Hint

   Consider the polynomial form that matches F(n).

6. 6.

   Demonstrate how to apply the theorem to find particular solutions of a recurrence: a(n) = a(n-1) + 5 with a(0) = 1.

   Hint

   Look at the constant terms in your guesses.