Question

(200+1)(200-2)(200+3)(200-4)....(200+2018)(200-2019)

Answer 1

Кароче суть в том, что всегда ответ будет 199. Я не особо поняла, что нужно сделать, так что могу написать только то, что ответ будет 199
Удачи:-)

Answer 2

To simplify the expression $(200+1)(200-2)(200+3)(200-4)\ldots(200+2018)(200-2019)$, you can use the difference of squares factorization:

$(a+b)(a-b) = a^2 - b^2$

In your expression, $a = 200$ and $b$ is a sequence of numbers starting from 1 and increasing by 1 up to 2018. So you can rewrite the expression as:

$(200+1)(200-2)(200+3)(200-4)\ldots(200+2018)(200-2019) = 200^2 - 1^2 - 2^2 + 3^2 - 4^2 + \ldots - 2018^2 + 2019^2$

Now, you need to calculate this expression. It involves a long list of squares and subtractions. Calculating it manually would be quite tedious, but you can use a calculator or a programming tool to compute the result:

$$\begin{align*} &200^2 - 1^2 - 2^2 + 3^2 - 4^2 + \ldots - 2018^2 + 2019^2 \\ &= 40000 - 1 - 4 - 9 - 16 + \ldots - 4072324 + 4072361 \end{align*}$$

After calculating this expression, you will have the final result. It's a time-consuming process, so using a calculator or a computer program is the most practical way to find the answer.