The given statement is is divisible by 7.

When n = 1,

.

7 is divisible by 7 , the statement is true for n = 1.

Assume that is divisible by 7 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 8)

                 (Multiply: )

        (Subtract 1 from each side)

              (Subtract: )

          (Take out common factor)

Since r whole number, is a whole number.

Therefore is divisible by 7.

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

This Proves that is divisible by 7 for all positive integers n.

is divisible by 7 for all positive integers n.