16.6.1. Recurrence Condition

Try these first

1. 1.

   What is a recurrence relation?

   Hint

   Think about how sequences can be defined based on previous terms.

2. 2.

   Provide an example of a strictly increasing sequence.

   Hint

   Consider a sequence of numbers that continuously get larger.

3. 3.

   What defines a strictly increasing sequence?

   • Each term is equal
   • Each term is greater than the previous one
   • Each term is a whole number

   Hint

   Think about how the numbers in the sequence relate to one another.

4. 4.

   True or False: Initial conditions are not needed to calculate recurrence relations.

   • True
   • False

   Hint

   Consider where you would begin calculations.

5. 5.

   If you have a sequence of strictly increasing integers from 1 to n, how many valid sequences can you construct where the second last number can't exceed n-1?

   Hint

   Think about how many terms are available and apply your understanding of the sequence definitions.

6. 6.

   Using your knowledge of the relationship between f(n) for combinations with initial conditions, calculate values for n up to 5.

   Hint

   Remember to build upon each previous result step-by-step.