1. Determine the proposition to prove: First, you need to be clear about what you want to prove. This proposition should be a statement about the natural number n, such as "2n+ 1 is always odd for all natural numbers n".
2. Set the basic situation: Then, you need to set a basic situation, that is, when n is 0 or 1. This is your first inductive hypothesis.
3. Write down the induction steps: Next, you need to write out how to transition from the basic situation to a more general situation to prove it. This usually involves replacing the original n with n+ 1, adjusting your premise and ensuring that the new situation still meets your original statement.
4. Verify the entry steps: Finally, you need to check whether your entry steps are correct. This usually includes using basic situations to test whether your induction steps can produce correct results.
5. Conclusion: If all the inductive steps are verified, then you can come to the conclusion that your original proposition holds true for all natural numbers.
Note: Mathematical induction does not guarantee correct results in all cases. For example, it cannot be used to prove some propositions involving infinite sets. In addition, some propositions may hold true for some natural numbers, but not for others. In these cases, you need to use other proof methods.