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FAQs on JEE Mains Previous Year Questions (2021-2024): Mathematical Induction - Mathematics (Maths) for JEE Main & Advanced
| 1. How do you prove a statement using mathematical induction? |  |
Ans. To prove a statement using mathematical induction, you typically follow these steps:
1. Prove the base case (usually when n = 1).
2. Assume the statement holds for an arbitrary positive integer k.
3. Use this assumption to prove that the statement also holds for k+1.
| 2. What is the principle of mathematical induction? | |
Ans. The principle of mathematical induction states that if a statement holds for a base case (usually when n = 1) and if it can be shown that whenever the statement is true for a particular positive integer k, it must also be true for k+1, then the statement is true for all positive integers.
| 3. Can mathematical induction be used to prove inequalities? | |
Ans. Yes, mathematical induction can be used to prove inequalities. To do this, you would follow the same steps as in a regular mathematical induction proof, but instead of proving that a statement is true, you would prove that an inequality holds for all positive integers.
| 4. What are some common mistakes to avoid when using mathematical induction? | |
Ans. Some common mistakes to avoid when using mathematical induction include:
- Forgetting to prove the base case.
- Incorrectly assuming the statement is true for k+1 without proving it.
- Using circular reasoning.
- Making arithmetic errors in the inductive step.
| 5. Can mathematical induction be used to prove divisibility properties? | |
Ans. Yes, mathematical induction can be used to prove divisibility properties. By following the principles of mathematical induction, you can show that a certain property related to divisibility holds true for all positive integers.
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