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.

If then .

Since ,  is also true.

From (1) and (2):

 is true for

The final statement is exactly , so is true.

Because is true for and implies , is true for and so on.

That is, by the principle of mathematical induction,

is true integer values .

is true integer values .