What's the problem? Just want to know about mathematical induction? Baidu, then.

Basic steps

(A) the first mathematical induction:

Generally speaking, to prove a proposition related to a positive integer n, there are the following steps:

(1) proves that the proposition holds when n takes the first value, and the general series takes 1, but there are some special cases;

(2) Assuming that the proposition holds when n = k(k ≥[ n the first value of n], and k is a natural number), it is proved that the proposition also holds when n=k+ 1.

(2) the second mathematical induction:

For a proposition related to natural numbers,

(1) Verify that P(n) holds when n=n0;

(2) Assuming no.

Composition (1)(2) holds for all natural numbers n(≥n0) and proposition P(n);

(3) Backward induction:

(1) Proposition P(n) holds for infinite natural numbers;

(2) Assuming that P(k+ 1) holds, and on this basis, it is deduced that P(k) holds,

Comprehensive (1)(2), for all natural numbers n (>; N0), the proposition P(n) is true;

Spiral induction

P(n) and Q(n) are two propositions related to natural numbers. Suppose.

(1)P(n0) holds;

(2) suppose p (k) (k >; N0) holds, Q(k) holds, assuming Q(k) holds, P(k+ 1) holds;

Comprehensive (1)(2), for all natural numbers n (>; N0), P(n) and Q(n) all hold;