1, (inductive basis) proves that the proposition holds when n takes the first value n0(n0∈N*);

2. (Inductive recursion) Assuming that n = k (k ≥ n0, k∈N*), it is proved that the proposition is also true when n = k+ 1

The principle of this method lies in: first, prove that the proposition is valid at a certain initial value, and then prove that the process from one value to the next is valid. When these two points are proved, then any value can be deduced by repeatedly using this method.

Extended data

Proof without inductive hypothesis is not mathematical induction. In the process of proving n = k to n = k+ 1, it is difficult to find the changing law of n = k to n = k+ 1. The key to the breakthrough is to clearly analyze the differences and relations between p(k) and P (k+ 1).

P (k) and P (k+ 1) are separated by means of decomposition, addition, combination, amplification and contraction. There are many methods to prove inequality. In the process of proving inequality by mathematical induction, we should flexibly use methods such as comparison, amplification and analysis.

Baidu Encyclopedia-Mathematical Induction