Principle of Mathematical Induction (PMI)

(i) P(1) is true

(ii) P(r) is true P(r+1) is true.

Algorithm for proving a statement by P.M.I

Step I:

Denote the statement involving natural numbers n = 1, 2,…. by P(n).

Step II:

Prove that the statement P(1) holds good by putting n = 1 on one side of the statement and then simplifying it to take the form of the expression on the other side.

Step III:

Assume that the statement p(n) is true for n = r, i.e., P(r) is true.

Step IV:

Use the assumption p(r) is true, to prove p(r+1) is true.