Proof steps:
1. Verify that n=n0 holds (n0 is the initial value of n).
2. Assuming that the original proposition holds when n = k, it is proved that n = k+ 1 also holds.
3. It is concluded that the original example holds for all natural numbers with n≥n0.
Matters needing attention in the certificate:
1 and n=n0 must be verified. This step is called inductive basis (equivalent to knocking down the first domino).
2. The key step is to assume that the original proposition holds when n = k, and then prove that n = k+ 1 also holds. This step is called inductive hypothesis (the function is to prove that there is such a law between any two adjacent dominoes: the first one falls, and the last one must fall), and this step is also the most difficult.
3. In the process of proving that n = k+ 1 is also true, we must use the hypothetical conclusion.
4. In the process of proving that n = k+ 1 is also true, we should pay attention to two points: first, find the form of hypothesis, so as to use the conclusion of hypothesis, and then find the form of proof result.
5, when n = k+ 1, we should pay full attention to the difference with n = k, increase or decrease.