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Mathematical first induction
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 method: when the initial verification needs to verify n= 1, 2, 3,, m, the conclusion holds; 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

The first mathematical induction is common, and the second mathematical induction is very useful in proving the general formula of Fibonacci sequence (m=2).

2. Essential differences

The conclusion that the first mathematical induction can prove, the second mathematical induction is unnecessary. The conclusion that can be proved by the second mathematical induction is not necessarily effective by the first mathematical induction.

3. The proof process is different.

If the second mathematical induction is adopted, suppose n

References:

Baidu encyclopedia-the first mathematical induction

Baidu encyclopedia-the second mathematical induction