Question

Алгоритм вычисления значения функции F(n), где n — натуральное число, задан следующими соотношениями: F(1)=1, F(n)=F(n−1)⋅n,приn>1 . Чему равно значение функции F(8)?

Answer 1

F(2) = 2
F(3) = 6
F(4) = 24
F(5) = 120
F(6) = 720
F(7) = 5040
F(8) = 40320

Answer 2

Algorithm for Calculating the Value of Function F(n)

The algorithm for calculating the value of function F(n), where n is a natural number, can be defined using the following recursive relationship:

- F(1) = 1 - F(n) = F(n-1) * n, for n > 1

To calculate the value of F(8), we can apply the algorithm step by step:

1. Start with the base case: F(1) = 1. 2. Use the recursive relationship to calculate F(2): F(2) = F(1) * 2 = 1 * 2 = 2. 3. Use the recursive relationship to calculate F(3): F(3) = F(2) * 3 = 2 * 3 = 6. 4. Use the recursive relationship to calculate F(4): F(4) = F(3) * 4 = 6 * 4 = 24. 5. Use the recursive relationship to calculate F(5): F(5) = F(4) * 5 = 24 * 5 = 120. 6. Use the recursive relationship to calculate F(6): F(6) = F(5) * 6 = 120 * 6 = 720. 7. Use the recursive relationship to calculate F(7): F(7) = F(6) * 7 = 720 * 7 = 5040. 8. Use the recursive relationship to calculate F(8): F(8) = F(7) * 8 = 5040 * 8 = 40320.

Therefore, the value of the function F(8) is 40320.

Please note that this algorithm uses recursion to calculate the value of F(n) based on the previous value F(n-1). Each step multiplies the previous value by the current value of n.