Mathematical Induction
* A statement that has a definite truth value, that is, true or false, is called a mathematical statement.
* Deductive reasoning involves logical steps to arrive upon a particular case from a general case.
* An Inductive reasoning is the counter part of deductive reasoning.
* The principle used to prove mathematical statements, formulae and results involving positive integers are called the principle of mathematical induction.
Application of Mathematical Induction
* The principles of mathematical induction:
Let P (n) be a statement, where n is a natural number, such that:
* The statement is true for n = 1 or P (1) is true.
* If the segment is true for n = k, where k is a positive integer, then the statement is also true for
n = k + 1. P (k) is true ⇒ P (k + 1) is true.
* Then, P (n) is true for all natural numbers n.