Principle of Mathematical Induction is a method or process using which one can find whether a given statement is true for all the natural Numbers or not. Natural numbers are the ordinary counting numbers like 1, 2, 3, 4 and so on. These numbers are also referred as the positive integers or non-negative Integer’s means only positive numbers are included.
The simplest form of mathematical induction identify that whether a statement which is included is a natural number n which holds for all values of n is either true or not. The Proof of Mathematical Induction contains two steps which are shown below:
1. The basic case of induction mathematical is used to show whether a statement holds the value of n is equal to the lowest value of n. Generally, we take the value of n as 0 or 1.
2. The inductive case of mathematical induction is used to show whether the given statement holds the value of n then the full statement also holds when the value of n is substituted to n + 1.
This given method is applicable by proving the statement is true for the starting value. Then we have to prove the process which is used to go from one value to the other value which is valid. If both the given values are taken, then any value can be calculated by performing the process.
Let us use the principle of mathematical induction is to prove the following statement:
When we have A(n) = 0 + 1 + 2 + 3 + …… + n = n (n + 1) / 2;
Assume that we have the value of n is ‘1’, then putting the value of n in the formula we get:
= n (n + 1) / 2;
n = 1;
A (1) = 1 (1 + 1) / 2;
So we get the value of left and right hand side same.