Mathematical Induction Steps
Various steps used in Mathematical Induction are named accordingly. The names of the various steps used in the principle of mathematical induction are,
- Base Step: Prove P(k) is true for k =1
- Assumption Step: Let P(k) is true for all k in N and k > 1
- Induction Step: Prove P(k+1) is true using basic mathematical properties.
If the above three steps are proved then we can say that “By the principle of mathematical induction, P(n) is true for all n belonging to N”.
Principle of Mathematical Induction
Mathematical induction is a concept in mathematics that is used to prove various mathematical statements and theorems. The principle of mathematical induction is sometimes referred to as PMI. It is a technique that is used to prove the basic theorems in mathematics which involve the solution up to n finite natural terms.
Principle of Mathematical Induction is widely used in proving various statements such as a sum of first n natural numbers is given by the formula n(n+1)/2. This can be easily proved using the Principle of Mathematical Induction.
In this article, we will learn about the principle of mathematical induction, its statement, its example, and others in detail.
Table of Content
- What is Mathematical Induction?
- Principle of Mathematical Induction Statement
- Mathematical Induction Steps
- Mathematical Induction Example