Question

Можно ли записать 2022 числа в ряд так, что сумма любых пяти подряд в этом ряду окажется положительной, а сумма всех отрицательной. Ответ обоснуйте. Пожалуйста, очень срочно

Answer 1

Ответ:

Можно

Пошаговое объяснение:

Напишем так:

A = 136 - 543 + 136 + 136 + 136 + 136 - 543 + 136 + 136 + 136 + ...  

... + 136 - 543 + 136 + 136 + 136 + 136 - 543

Это выражение можно сгруппировать так:

A = (136 - 543 + 136 + 136 + 136) + (136 - 543 + 136 + 136 + 136) + ...  

... + (136 - 543 + 136 + 136 + 136) + 136 - 543 =

= (544 - 543) + (544 - 543) + ... (544 - 543) + 136 - 543 =

= 1 + 1 + ... + 1 + 136 - 543 = 1*404 + 136 - 543 = 540 - 543 = -3

Здесь всего 2022 слагаемых, то есть 2022 = 404*5 + 2.

То есть 404 группы по 5 слагаемых, и еще 2 слагаемых в конце.

Если мы возьмем любую группу из 5 слагаемых, то в ней будет 4 числа 136 и одно (-543). В сумме они дают 4*136 - 543 = 544 - 543 = 1.

А сумма всех 2022 слагаемых дает отрицательное число -3.

Это наибольшее отрицательное значение такой суммы.

Answer 2

Can 2022 be written in a sequence such that the sum of any five consecutive numbers is positive, while the sum of all the numbers is negative?

To determine if it is possible to write the number 2022 in a sequence such that the sum of any five consecutive numbers is positive while the sum of all the numbers is negative, we need to analyze the properties of the number 2022 and the conditions given.

Let's consider the conditions given: 1. The sum of any five consecutive numbers should be positive. 2. The sum of all the numbers should be negative.

To satisfy the first condition, we need to ensure that any five consecutive numbers in the sequence have a positive sum. This means that the numbers in the sequence should be carefully chosen to create positive sums when taken in groups of five.

To satisfy the second condition, the sum of all the numbers in the sequence should be negative. This means that the overall sum of the numbers should be negative, regardless of the grouping.

Now, let's analyze the number 2022. The number 2022 is a positive integer. To create a sequence with a negative overall sum, we need to introduce negative numbers into the sequence. However, since the sum of any five consecutive numbers should be positive, it is not possible to create a sequence with the given conditions using only positive and negative integers.

Therefore, it is not possible to write the number 2022 in a sequence such that the sum of any five consecutive numbers is positive while the sum of all the numbers is negative.

In conclusion, it is not possible to write the number 2022 in a sequence that satisfies the given conditions.