N); such that:
- P(1) is true and
- truth of P(k) implies the truth of P(k+1), then by the principle of
mathematical induction (P.M.I.), the statement P(n) is true for n 
N.
Working rules for using P.M.I.
Step 1:
Show that the result holds for n = 1.
Step 2:
Assume the validity of the result for n equal to some arbitrary but fixed natural number, say, k.
Step 3:
Show that the result holds for n = k+1.
Step 4:
Conclude that the result holds for all natural numbers.
Using Principle of Mathematical Induction
For any natural number n, prove that
Proof:
We shall use PMI to prove that
Step 1:
Let n = 1
(1) is true for n = 1.
Step 2:
Let (1) be true for n = k
…(2)
Step 3:
Let n = k + 1
LHS of (1)
R.H.S of (1)
\ (1) is true for n = k + 1.
By P.M.I., we have
