Question

What one of the following equations or inequalities best illustrates the "recursive structure" of a factorial formula?

(a). K！= 2！+ K！-2
(b). (K+1)！= K！+ 1！
(c). 0！= 1
(d). ( k + 1 )！= ( k + 1 ) * K！
(e). K！≥ K

Answer 1

The equation (k + 1)！= (k + 1) * k！ best illustrates the recursive structure of a factorial, where each factorial is calculated based on the previous one multiplied by the new element.

Step-by-step explanation:

The question asks which equation or inequality best exemplifies the recursive nature of a factorial. Out of the given options, choice (d), (k + 1)！= (k + 1) * k！, clearly reflects the recursive structure of a factorial formula. When calculating the factorial of a number, you multiply that number by the factorial of the number immediately preceding it. For example, 4! = 4 * 3!, and this process can be iterated down until you reach the base case, which is 0! = 1, as defined typically in mathematics for the factorial function.