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What is the difficulty of mathematical induction? How to practice induction at ordinary times?
To understand mathematical induction, it is strongly recommended to play dominoes and learn the essence from them! ! !

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.