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