# Summary

**Principle of Mathematical Induction:**

Corresponding to each positive integer

If (i) P(1) is true, and

(ii) P(

Then P(

*n*let there be a statement or a proposition P(*n*).If (i) P(1) is true, and

(ii) P(

*k*+1) is true wherever P(*k*) is true, [Where*k*is a positive integer]Then P(

*n*) is true for all positive integers*n*.**Working rules for using principle of mathematical induction:**

Step (1) : Show that the result is true 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 is also true for n = k + 1.

Step (4) : Conclude that the result holds for all natural numbers.

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 is also true for n = k + 1.

Step (4) : Conclude that the result holds for all natural numbers.