For the product of k consecutive integers, which of the following is true?

The product of ( k ) consecutive integers, denoted as ( n \times (n+1) \times (n+2) \times \ldots \times (n+k-1) ), will always yield a value greater than ( k ) when ( n ) begins at 1 or any positive integer. This is because the smallest product occurs starting from the first positive integer (1), where the product of, for example, 3 consecutive integers is ( 1 \times 2 \times 3 = 6 ), which is greater than 3.

As ( n ) increases, the product increases even more significantly, especially as ( k ) grows larger than 2. The nature of consecutive integers, encompassing both minimum and maximum values within and extending beyond ( n ), generally ensures that the product accelerates beyond just ( k ).

In cases where ( n ) starts from zero or is negative, the product may still exceed ( k ) in absolute value. For instance, if ( n = -1 ) and ( k = 2 ), the integers would be ( -1 ) and ( 0 ), resulting in a product of (