Which of the following best illustrates the concept of 'mathematical induction'?
Practice Questions
1 question
Q1
Which of the following best illustrates the concept of 'mathematical induction'?
Proving a statement for all integers by showing it holds for 1 and assuming it holds for n to prove for n+1.
Using a counterexample to disprove a statement.
Establishing a formula through empirical observation.
Demonstrating a theorem through geometric construction.
Mathematical induction is a method of proof that involves proving a base case and then showing that if the statement holds for an arbitrary case n, it holds for n+1.
Questions & Step-by-step Solutions
1 item
Q
Q: Which of the following best illustrates the concept of 'mathematical induction'?
Solution: Mathematical induction is a method of proof that involves proving a base case and then showing that if the statement holds for an arbitrary case n, it holds for n+1.
Steps: 5
Step 1: Understand that mathematical induction is a way to prove statements about numbers, usually natural numbers (1, 2, 3, ...).
Step 2: Start with a base case. This is the simplest case, often n=1, and you show that the statement is true for this case.
Step 3: Assume the statement is true for some arbitrary case n. This is called the 'inductive hypothesis'.
Step 4: Show that if the statement is true for n, then it must also be true for n+1. This is called the 'inductive step'.
Step 5: Conclude that since the base case is true and the inductive step holds, the statement is true for all natural numbers.
