Question

1+2-3-4+5+6-7-8+...2019​

Answer 1

1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + ...2019 = ?

1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + ... - 2016 + 2017 + 2018 - 2019 = ?

Можно заметить, что

1 + (2 - 3) + (-4 + 5) + (6 - 7) + ... + (-2016 + 2017) + (2018 - 2019) = 1 - 1 + 1 - 1 + ... + 1 - 1 = 0

Ответ: 0

Answer 2

1+2-3-4+5+6-7-8+2019

1)1+2=3

2)3-3=0

3)0-4=-4

4)-4+5=1

5)1+6=7

6)7-7=0

7)0-8=-8

8)-8+2019=2011

Answer 3

To calculate the value of the expression 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + ... + 2019, we can group the terms in pairs as follows:

(1 + 2) - (3 + 4) + (5 + 6) - (7 + 8) + ... + (2019)

Now, each pair inside the parentheses can be simplified:

(1 + 2) = 3 (3 + 4) = 7 (5 + 6) = 11 (7 + 8) = 15 ...

We can observe that the pattern for the sum of each pair is: 3, 7, 11, 15, and so on, with increments of 4 between each sum.

Now, let's find the number of pairs. We want to find the number of pairs of the form (a + b), where a and b are consecutive positive integers, such that the last term in the pair, b, is less than or equal to 2019.

The last term in a pair, b, can be represented as:

b = a + 1

Now, we want to find the maximum value of a that satisfies the condition b ≤ 2019:

a + 1 ≤ 2019 a ≤ 2019 - 1 a ≤ 2018

So, the maximum value of a is 2018.

Now, the number of pairs (a + b) can be calculated using the formula for the sum of an arithmetic series:

Number of pairs = (last term - first term) / common difference + 1 = (2018 - 3) / 4 + 1 = 2015 / 4 + 1 = 504 + 1 = 505

Now, we have 505 pairs with a sum of 3, 7, 11, 15, and so on.

The sum of these pairs can be found using the formula for the sum of an arithmetic series:

Sum of pairs = Number of pairs * (first term + last term) / 2 = 505 * (3 + 2018) / 2 = 505 * 2021 / 2 = 509525

So, the value of the expression 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + ... + 2019 is 509,525.