Practice Proof By Induction (14.2) - Lecture -14 - Discrete Mathematics - Vol 1
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Proof by Induction

Practice - Proof by Induction

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Practice Questions

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Question 1 Easy

What are the two main steps in a proof by induction?

💡 Hint: Think about the first step in proving something is true.

Question 2 Easy

What is the base case for proving that the arithmetic mean is at least the geometric mean for 2 numbers?

💡 Hint: Consider two positive integers and their means.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the purpose of the base case in proof by induction?

To prove the statement for all integers
To establish the truth for one initial case
To derive a general formula

💡 Hint: Remember that every proof needs a starting point to build upon.

Question 2

A celebrity in a party knows everyone but is not known by anyone.

True
False

💡 Hint: Think about the social dynamics of knowing someone.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove using induction that for every n > 1, n! > 2^n.

💡 Hint: Consider how quickly factorial values grow compared to powers!

Challenge 2 Hard

Prove that for any integer n, n² + n is even.

💡 Hint: Factor to see the evenness clearly.

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