#### Answer

The principle of mathematical induction states that a statement involving positive integers is true for all positive integers when two conditions have been satisfied:
The first condition states that the statement is true for the positive integer $1$.
The second condition states that if the statement is true for some positive integer $ k $, it is also true for the next positive integer $ k+1$.

#### Work Step by Step

We know that the principle of mathematical induction is as follows:
Assume ${{S}_{n}}$ to be a statement involving the positive integer $ n $. If
(1) ${{S}_{1}}$ is true and
(2) The truth of the statement ${{S}_{k}}$ implies the truth of the statement ${{S}_{k+1}}$, for every positive integer $ k $.
Then we can prove the statement ${{S}_{n}}$ is true for all positive integers $ n $ .