19.2.7. Summary and References

Try these first

1. 1.

   What is a linear non-homogeneous recurrence equation?

   Hint

   Think about how these terms are structured.

2. 2.

   Define the associated homogeneous recurrence relation.

   Hint

   What does it leave you with?

3. 3.

   What is the general form of a linear non-homogeneous recurrence equation?

   • a(n) = c_1*a(n-1) + c_2*a(n-2) + F(n)
   • a(n) = F(n)
   • a(n) = 2*a(n-1)

   Hint

   Look for the version that includes both previous terms and F(n).

4. 4.

   True or False: A homogeneous equation does not include any function F(n).

   • True
   • False

   Hint

   Consider the definitions we've discussed.

5. 5.

   Given the recurrence relation a(n) = 2*a(n-1) + n^2, derive the general solution.

   Hint

   Focus on the polynomial degree and ensure your guesses are structured correctly.

6. 6.

   If F(n) includes an exponential function not part of the characteristic roots, how would you derive the particular solution?

   Hint

   What structures might connect well without duplicating characteristics?