What is the primary purpose of using 'mathematical induction'?
Practice Questions
1 question
Q1
What is the primary purpose of using 'mathematical induction'?
To prove statements for all natural numbers
To derive formulas for geometric shapes
To calculate limits of functions
To solve quadratic equations
Mathematical induction is primarily used to prove statements that are asserted for all natural numbers.
Questions & Step-by-step Solutions
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Q
Q: What is the primary purpose of using 'mathematical induction'?
Solution: Mathematical induction is primarily used to prove statements that are asserted for all natural numbers.
Steps: 6
Step 1: Understand that mathematical induction is a method used in mathematics.
Step 2: Recognize that it is used to prove statements or formulas that are claimed to be true for all natural numbers (like 1, 2, 3, ...).
Step 3: Know that the process involves two main parts: the base case and the inductive step.
Step 4: The base case shows that the statement is true for the first natural number (usually 1).
Step 5: The inductive step shows that if the statement is true for one natural number (let's say n), then it must also be true for the next number (n + 1).
Step 6: If both parts are proven, we conclude that the statement is true for all natural numbers.
