Question 233402
Assuming n must be an integer (or a whole number or a natural number), here the keys to this problem:<ul><li>All even numbers are divisible by two.<li>Whenever integers are multiplied, if one or more of the numbers is even, then product will be even.</li><li>If n is even, n+1 will be odd. Or if n is odd, then n+1 will be even. The point is that either n or n+1 <i>must</i> be an even number.</li><li>So n(n+1)(2n+1) must be even.</li><li>So n(n+1)(2n+1) must be divisible by 2.</li></ul>
The answer is definitely not (e). I cannot find any way to show that n(n+1)(2n+1) is always divisible by anything but 2 so I believe the answer is (a).