Question

For the product n(n + 1)(2n + 1), n ∈ N, which one of the following is not necessarily true?
a. It is even
b. Divisible by 3
c. Divisible by the sum of the square of first n natural numbers
d. Never divisible by 237

Answer 1

Clearly the expression is basically the formula for sum of 1st n squares but without the "6" in the denominator.

So options 1,2,4 are true.

And about 237  

The above expression will obviously be divisible by 237

When n= 237 as it will be 237*238*475 In fact even for n = 236 and n = 118 it will be divisible by 237.

If there is any confusion please leave a comment below.