Prove that is true for all positive integers .

Let be the statement that .

Verify that is true for .

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is true for .

Assume that is true for .

Substitute in .

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is true for positive integer .

Show that must be true.

Consider . \ \

Add next term on each side.

.

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,

  or is true for all positive integers .

By the principle of mathematical induction, or is true for all positive integers .