Mathematical Induction

Mathematical induction is a form of direct proof, usually done in two steps. When trying to prove a given statement for a set of natural numbers, the first step, known as the base case, is to prove the given statement for the first natural number. The second step, known as the inductive step, is to prove that, if the statement is assumed to be true for any one natural number, then it must be true for the next natural number as well. Having proved these two steps, the rule of inference establishes the statement to be true for all natural numbers. In common terminology, using the stated approach is referred to as using the Principle of mathematical induction.

1. For the base case, let n=1, that means it takes 1 as the starting point of the range value.

2. After you assumed it is true when n=k, you can see n=k+1, that means the range of possible values of the value extends infinitely, otherwise, that means the range of possible values of the value extends to the negative infinity.

3. When you do assumption, you can add up or subtract to be standard for each unit.

4. After you assumed it is true when n=k, you can see n=k+1, the value is 1, that means for all integer.