WHAT PMI MEAN..?
Hi!
Here is the answer to your query.
Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural number.
The principle of mathematical induction can be stated as
Suppose there is a given statement P(n) involving the natural number n such that
(i) The statement is true for n = 1, i.e., P(1) is true, and
(ii) If the statement is true for n = k (where k is some positive integer), then the statement is true for n = k + 1, i.e., truth of P(k) implies the truth of P(k + 1).
Then, P (n) is true for all natural numbers n.
Suppose there is a given statement P(n) involving the natural number n such that
(i) The statement is true for n = 1, i.e., P(1) is true, and
(ii) If the statement is true for n = k (where k is some positive integer), then the statement is true for n = k + 1, i.e., truth of P(k) implies the truth of P(k + 1).
Then, P (n) is true for all natural numbers n.
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Hence, by the principle of mathematical induction, statement P(n) is true for all natural numbers n.
Cheers!