19.2.6. Unification of Examples and General Theorem Statement

Try these first

1. 1.

   Define a linear non-homogeneous recurrence equation.

   Hint

   Consider how terms are related.

2. 2.

   What represents associated homogeneous equations?

   Hint

   Focus on just the previous terms.

3. 3.

   What is the purpose of forming the associated homogeneous equation?

   Hint

   Reflect on simplifying the original equation.

4. 4.

   True or False: A particular solution can be found by simply stating a number.

   • True
   • False

   Hint

   Consider what defines a solution.

5. 5.

   Solve the recurrence relation T(n) = 2*T(n-1) + F(n) where F(n) is n^2. Describe your steps in detail.

   Hint

   Focus on the structure of F(n) and adjust your guesses appropriately.

6. 6.

   If F(n) = 5*n^3 and the homogeneous solution has repeated roots, determine the particular solution.

   Hint

   Link the degree of F(n) to the possible multiplicity adjustment.