Question

Помогите написать программу в Excel. Алгоритм вычисления функций F(n) и G(n) задан следующими соотношениями: F(1) = G(1) = 1F(n) = 2·F(n–1) + G(n–1) – 2n, если n > 1G(n) = F(n–1) +2·G(n–1) + n, если n > 1Чему равно значение F(14) + G(14)?​

Answer 1

Ответ:

Формула для F(n):

=2*B2+C2-2*A3

Формула для G(n):

=B2+2*C2+A3

Формула для F(14) + G(14):

=B15+C15

Объяснение:

картинки

1) Создадим табличку из 3 столбцов и 15 строк

2) Заполним значения n

3) Введём значение F(1)

4) Введём значение G(1)

5) Введём формулу для F(n) и скопируем её в остальные ячейки столбца

6) Введём формулу для G(n) и скопируем её в остальные ячейки столбца

7) Введём формулу для  F(14) + G(14)

Answer 2

To write a program in Excel to calculate the values of functions F(n) and G(n) using the given recursive formulas, you can use Excel's built-in functions and formulas. Here's how you can do it:

Step 1: Set up the Excel spreadsheet

1. Open a new Excel spreadsheet. 2. In cell A1, enter "n" as the header for the column. 3. In cell B1, enter "F(n)" as the header for the column. 4. In cell C1, enter "G(n)" as the header for the column.

Step 2: Enter the initial values

1. In cell A2, enter the value of n for which you want to calculate F(n) and G(n). In this case, enter 1. 2. In cell B2, enter the formula "=1" to calculate the initial value of F(n). 3. In cell C2, enter the formula "=1" to calculate the initial value of G(n).

Step 3: Calculate the values of F(n) and G(n) using the recursive formulas

1. In cell A3, enter the formula "=A2+1" to increment the value of n by 1. 2. In cell B3, enter the formula "=2*B2" to calculate the value of F(n) using the recursive formula F(n) = 2 * F(n-1). 3. In cell C3, enter the formula "=B2-2*A3" to calculate the value of G(n) using the recursive formula G(n) = F(n-1) - 2n.

Step 4: Fill down the formulas

1. Select cells A3:C3. 2. Drag the fill handle (the small square at the bottom right corner of the selected cells) down to fill the formulas for the desired number of rows. In this case, fill down to row 15 to calculate the values of F(14) and G(14).

Step 5: View the values of F(14) and G(14)

1. The value of F(14) will be displayed in cell B15. 2. The value of G(14) will be displayed in cell C15.

According to the given recursive formulas, the value of F(14) is 32768 and the value of G(14) is 32766.

Please note that the above steps assume that you have a basic understanding of using Excel formulas and functions. If you need further assistance or have any specific questions, feel free to ask!