1. Topic 1(COLON) Mathematical Proof and Reasoning

Lesson 1.4: Induction With Sequences, Inequalities And Matrices — Quiz

Test your understanding of lesson 1.4: induction with sequences, inequalities and matrices with 5 practice questions.

Practice Questions

Question 1

What is the first step in proving a statement by mathematical induction?

Question 2

In the context of mathematical induction, what does the inductive step involve?

Question 3

For the sequence defined recursively by $a_n = 3a_{n-1} + 2$ with a base case $a_1 = 1$, what is the base case value of $a_1$?

Question 4

How can one prove the inequality $n^2 < (n + 1)^2$ for all positive integers $n$ using induction?

Question 5

Which property must a statement have for it to be proved false by a counterexample?