Question

Вычислите: 1) -8 + 9 - 10 + 11 - 12 + 13 - 14 + 15 - 16 + 17 - 18 + 19;2) 1 - 2 + 3 - 4 + 5 - 6+ ... + 99 - 100.​

Answer 1

Ответ:

1)6 2)-50

Пошаговое объяснение:

1)каждая пара берется как +1,т.е.

-8+9 = 1

-10+11 = 1 и тд

и получаем: 1+1+1+1+1+1 = 6

2)каждую пару берем как -1

1-2 = -1

3-4 = -1 и тд

получаем -1*(100/2) = -50

100/2 т.к. всего чисел 100 а в паре 2 числа

Answer 2

Sure, let's calculate the expressions step by step:

1. -8 + 9 - 10 + 11 - 12 + 13 - 14 + 15 - 16 + 17 - 18 + 19

To simplify this, we can group the numbers in pairs:

= (-8 + 9) + (-10 + 11) + (-12 + 13) + (-14 + 15) + (-16 + 17) + (-18 + 19)

Now, perform the additions in each pair:

= 1 + 1 + 1 + 1 + 1 + 1

Now, add up the results:

= 6

So, the result of the first expression is 6.

2. 1 - 2 + 3 - 4 + 5 - 6 + ... + 99 - 100

This is an arithmetic sequence with a common difference of -1. We can find the sum of the first n terms in an arithmetic sequence using the formula:

Sum = (n/2) * (first term + last term)

In this sequence, the first term is 1, and the last term is 100. We need to find out how many terms (n) are there in this sequence.

The nth term of an arithmetic sequence can be found using the formula:

nth term = first term + (n - 1) * common difference

For this sequence, the nth term is 99 (the last term is 100, and the common difference is -1):

99 = 1 + (n - 1) * (-1)

Solve for n:

n - 1 = 99 - 1 n - 1 = 98 n = 99

So, there are 99 terms in this sequence. Now, let's calculate the sum:

Sum = (n/2) * (first term + last term) Sum = (99/2) * (1 + 100) Sum = 49.5 * 101 Sum = 4995

So, the sum of the second expression is 4995.

If you have any more math problems or questions, feel free to ask!