Mathematical Induction Summary

• A sentence is called a statement if it can be adjudged as true or false.

• Every statement is a sentence, but a sentence may or may not be a statement.

• A statement involving natural number n is generally denoted by P(n).

• Principle of mathematical induction states that if P(n) is a statement involving natural number n.

(i) P(1) is true i.e., the statement is true for n = 1.

(ii) Truth of P(k) implies the truth of P(k+1) i.e., the statement is true for n = k+1 assuming it to be true for n = k, then the statement P(n) is true for all natural numbers.