Question Detail
Question
P(n) = n(n²-1). Which of the following does not divide P(k + 1)?
Correct Answer
Option D is the correct answer.
Detailed Explanation
P(k+1) = (k+1)[(k+1)² - 1] = (k+1)(k² + 2k + 1 - 1) = (k+1)(k² + 2k) = (k+1)(k)(k+2). So P(k+1) = k(k+1)(k+2). This is clearly divisible by k, k+1, and k+2. It is not necessarily divisible by k+3.
Hint
Expand P(k+1) and factor completely.