What is the role of 'mathematical induction' in proofs?
Practice Questions
Q1
What is the role of 'mathematical induction' in proofs?
To prove statements for all integers
To establish the validity of geometric theorems
To solve algebraic equations
To analyze statistical data
Questions & Step-by-Step Solutions
What is the role of 'mathematical induction' in proofs?
Step 1: Understand that mathematical induction is a method used to prove statements that are true for all whole numbers (integers).
Step 2: Identify the statement you want to prove. This statement usually involves a variable, often denoted as 'n'.
Step 3: Establish the base case. This means you prove that the statement is true for the first integer, usually n = 1.
Step 4: Perform the inductive step. Assume the statement is true for some integer 'k'. This is called the 'inductive hypothesis'.
Step 5: Use the inductive hypothesis to prove that the statement is also true for the next integer, which is k + 1.
Step 6: Conclude that since the base case is true and the inductive step shows that if it is true for 'k', it is also true for 'k + 1', the statement is true for all integers.
