Question

1+3+3^2+...+3^9/1+3+3^2+...+3^4

Answer 1

Ответ: решение на фото.

Пошаговое объяснение:

Answer 2

To simplify the expression, let's first calculate the individual parts:

The sum of the geometric series 1 + 3 + 3^2 + ... + 3^9 can be calculated using the formula for the sum of a geometric series:

Sum = a * (r^n - 1) / (r - 1),

where: a = first term = 1, r = common ratio = 3, n = number of terms = 10 (1 + 3 + 3^2 + ... + 3^9).

So the sum of the geometric series is:

Sum = 1 * (3^10 - 1) / (3 - 1) = (59049 - 1) / 2 = 59048 / 2 = 29524.

Now let's calculate the sum of the geometric series 1 + 3 + 3^2 + ... + 3^4:

Sum = 1 * (3^5 - 1) / (3 - 1) = (243 - 1) / 2 = 242 / 2 = 121.

Now, the desired expression is:

(1 + 3 + 3^2 + ... + 3^9) / (1 + 3 + 3^2 + ... + 3^4) = 29524 / 121 ≈ 244.32231405 (rounded to 8 decimal places).