## Precalculus (6th Edition) Blitzer

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 $k+1$.
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 $n$ .