Problem description:

Please explain its principle in detail.

Analysis:

In the middle school mathematics textbooks and college entrance examination gardens, the mathematical induction used generally appears in the following forms:

1 pair'; Suppose "n is right", then "n+ 1 is right".

It should be pointed out that the above form is the basic form of mathematical induction, but it is not the only form.

The second mathematical induction can be summarized as follows

Specifically, it is divided into the following three steps:

(1) Basis: Prove that the proposition holds when n= 1;

(2) Inductive hypothesis: the proposition holds when n≤k; (That's the difference.)

(3) Inductive recursion: The proposition also holds when n=k+ 1 is deduced from inductive hypothesis.

Obviously, the difference between the second mathematical induction and the basic form of mathematical induction lies in inductive hypothesis.