Practice Example Of Strong Induction (12.2.8) - Induction - Discrete Mathematics - Vol 1
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Example of Strong Induction

Practice - Example of Strong Induction

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the base case for proving the statement that the sum of the first n integers is n(n + 1)/2?

💡 Hint: Evaluate the formula when n equals the smallest integer.

Question 2 Easy

Explain what regular induction is.

💡 Hint: Consider the two main steps involved in the process.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the first step in proof by induction?

Proving the inductive step
Establishing the base case
Concluding the proof

💡 Hint: Think about which step needs to be validated first.

Question 2

True or False: Strong induction only proves the existence of results for previous integers.

True
False

💡 Hint: Consider the scope of what strong induction allows.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove by induction that for all integers n ≥ 1, 2^n > n^2.

💡 Hint: Consider properties of exponential growth versus polynomial growth.

Challenge 2 Hard

Demonstrate that every amount of postal charges greater than 11 can be paid using 3-rupee and 5-rupee coins.

💡 Hint: Think about every integer in this case and how combinations transition logically.

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