13.9. Conclusion and Summary

Try these first

1. 1.

   Define a recurrence equation.

   Hint

   Think about sequences like Fibonacci.

2. 2.

   What does 'linear' mean in the context of recurrence relations?

   Hint

   Consider how the terms relate to each other mathematically.

3. 3.

   What is the essence of a recurrence equation?

   • A simple one-time calculation
   • An equation involving prior terms of a function
   • A graphical representation of data

   Hint

   Think about how sequences like the Fibonacci sequence are composed.

4. 4.

   Is it true that every recurrence equation has only one solution?

   • True
   • False

   Hint

   Remember how varying the start values influence outcomes.

5. 5.

   Given the recurrence relation T(n) = 2T(n/2) + n, solve for T(n) using the Master theorem.

   Hint

   Identify parameters a, b, and f(n) correctly.

6. 6.

   Propose a recurrence relation for a game where each player can either stay or move forward in a specific pattern, given initial conditions.

   Hint

   Look at the decisions influencing future game moves!