$\"\"$

Let $\"\"$ be the statement that $\"\"$ for $\"\"$ .

Consider the value of $\"\"$ : $\"\"$ .

$\"\"$

Thus, $\"\"$ is true.

Assume $\"\"$ is true, that $\"\"$ for $\"\"$ , where $\"\"$ is positive integer.

Prove that $\"\"$ must be true.

Use both the parts of inductive hypothesis.

$\"\"$

$\"\"$ is true for $\"\"$

The final statement is exactly $\"\"$ , so $\"\"$ is true.

Because $\"\"$ is true for $\"\"$ and $\"\"$ implies $\"\"$ , $\"\"$ is true for $\"\"$ and so on.

By the principle of mathematical induction, $\"\"$ is true integer values $\"\"$ .

$\"\"$

$\"\"$ is true integer values $\"\"$ .