Practice Combinatorial Proof Of Identity (16.7)

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define a valid sequence in your own words.
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Think about the properties that define a sequence.
Question 2.
What does the function $S(n)$ represent?
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Consider the meaning of sequences in increasing order.
3Question 3.
What is the form of the recurrence relation derived in this section?
- S(n) = S(n-1) + S(n-2)
- S(n) = 2S(n-1)
- S(n) = S(n-1) + S(n)
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Recall the formula discussed during the session regarding the last term.
4Question 4.
True or False: The number of valid sequences with $n=1$ is greater than with $n=2$ .
- True
- False
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Think back to the initial conditions we confirmed.
Question 5.
Given $n=4$ , calculate all differing valid sequences and confirm $S(4)$ .
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Consider each element's position and how many can fit in the sequence.
Question 6.
Explore how introducing another initial condition alters the recurrence.
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This involves checking sequences' sizes and corresponding counts.

4 more questions in this section. Enroll free to practise them all.