Multiplying both sides of( 1) by 2, we get 2 * 2 k > 2 * k i. e., 2 k + 1 > 2k or, 2 k + 1 > k + k or, 2 k + 1 > k + 1( since k > 1)
Therefore, P( k + 1) is true when P( k) is true. Hence, by principle of mathematical induction, P( n) is true for every positive integer n