Second, differences.

1, the difference in form

The first mathematical induction: as long as n= 1 (or n=0) is verified in the initial verification, the conclusion is established; The general assumption is that as long as n=k is assumed, the conclusion is also valid; On the basis of progressive recursion, it is deduced that the conclusion also holds when n=k+ 1

The second mathematical induction: when the initial verification needs to verify n = 1, 2, 3, ..., m; The general formula assumes that n = k+ 1, k+2, k+3, ..., k+m, and the conclusion is also valid; On the basis of progressive recursion, the conclusion is also valid when n=k+m+ 1

2. Use different methods

The first mathematical induction: The first induction is a special form of the second induction. Anyone who can use the first induction can use the second induction.

The second mathematical induction: the second induction can be proved, but the first induction may not be proved.

3. The proof process is different.

If the second mathematical induction is adopted, suppose n

Baidu encyclopedia-the first mathematical induction

Baidu encyclopedia-the second mathematical induction