Question

Гаусс (1+2+...399)-(1+2...+199)

Answer 1

Ответ:

(200+201+202...+399)

Пошаговое объяснение:

(1+2+...+399) - (1+2...+199) = (1+2...+199) - (1+2...+199) + (200+201+202...+399) = (200+201+202...+399)

Answer 2

To evaluate the expression "(1+2+...+399)-(1+2...+199)," we can simplify each part separately and then subtract the second part from the first.

The sum of an arithmetic series can be found using the formula: Sum = (n/2)(first term + last term), where n is the number of terms.

First, let's calculate the sum of the series 1+2+...+399:

Number of terms (n) = 399 First term = 1 Last term = 399

Sum_1 = (n/2)(first term + last term) = (399/2)(1 + 399) = 199(400) = 79,600

Next, let's calculate the sum of the series 1+2+...+199:

Number of terms (n) = 199 First term = 1 Last term = 199

Sum_2 = (n/2)(first term + last term) = (199/2)(1 + 199) = 99(200) = 19,800

Finally, we subtract Sum_2 from Sum_1:

Result = Sum_1 - Sum_2 = 79,600 - 19,800 = 59,800

Therefore, the value of the expression (1+2+...+399)-(1+2...+199) is 59,800.