The given statement is is divisible by 3.

When n = 1,

.

3 is divisible by 3, the statement is true for n = 1.

Assume that is divisible by 3 for some positive integer k.

That means there is a whole number r such that

Assume that the statement is true for some positive integer k, where k ≥ n.

This assumption is called the inductive hypothesis.

Show that the given equation is true for .

                              (Apply Inductive hypothesis)

                              (Add 1 to each side)

                  (Multiply each side by 4)

                       (Multiply: )

           (Subtract 1 from each side)

                 (Subtract: )

             (Take out common factor)

Since r whole number, is a whole number.

Therefore is divisible by 3.

Thus the statement is true for n = k + 1.

This Proves that is divisible by 3 for all positive integers n.