Let P(n) denotes that is divisible by 6, for each natural number n.
, which is divisible by 6. Therefore the result is true for n=1.
Now, assume that P(n) is true for n=k. That is for some m∈N. We have to prove that P(k+1) is also true.
Since is divisible by 22 for every even and odd k. Therefore is divisible by 66 and hence is divisible by 6. Therefore, is true whenever P(k) is true. Hence, by the principle of mathematical induction P(n) is true.