State the first principle of mathematical induction.

Let P(n) be a given statement involving the natural number n such that

(i) The statement is true for n = 1, i.e., P(1) is true (or true for any fixed natural number). This step is known as the Basis step.

(ii) If the statement (called Induction hypothesis) is true for n = k (where k is a particular but arbitrary natural number), then the statement is also true

for n = k + 1,

i.e, truth of P(k) implies the truth of P(k + 1). This step is known as the Induction (or Inductive) step.

Then P(n) is true for all natural numbers n.

Note: The first principle of mathematical induction states that if the basis step and the inductive step are proven, then P(n) is true for all natural numbers.