Practice Example Of Strong Induction (12.2.8) - Induction - Discrete Mathematics

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6 sample questions

Question 1.
What is the base case for proving the statement that the sum of the first n integers is n(n + 1)/2?
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Evaluate the formula when n equals the smallest integer.
Question 2.
Explain what regular induction is.
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Consider the two main steps involved in the process.
3Question 3.
What is the first step in proof by induction?
- Proving the inductive step
- Establishing the base case
- Concluding the proof
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Think about which step needs to be validated first.
4Question 4.
True or False: Strong induction only proves the existence of results for previous integers.
- True
- False
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Consider the scope of what strong induction allows.
Question 5.
Prove by induction that for all integers n ≥ 1, 2^n > n^2.
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Consider properties of exponential growth versus polynomial growth.
Question 6.
Demonstrate that every amount of postal charges greater than 11 can be paid using 3-rupee and 5-rupee coins.
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Think about every integer in this case and how combinations transition logically.

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