Question

1-3+5-7+............-99+101 .Срочно! !!

Answer 1

Ответ:

2500

Объяснение:

(1+99) + (3+97) + (5+95) + … + (47+53) + (49+51) = 25*100 = 2500

Или можно посчитать, как сумму последовательных членов арифметической прогрессии.

Первый член равен a₁=1,

разность прогрессии: d=2,

aₙ=99,

количество суммируемых членов: n = (aₙ - a₁)/d + 1= (99 - 1)/2 + 1 = 50

S = (aₙ + a₁)/2 * n = (99 + 1)/2 * 50 = 2500.

Answer 2

To find the sum of the series 1-3+5-7+...-99+101, we need to first determine the pattern and then calculate the sum.

The pattern in the series is that it alternates between adding and subtracting consecutive odd numbers:

1 - 3 + 5 - 7 + ... + 97 - 99 + 101

We can observe that the numbers are alternating between odd and even positions. The odd-positioned numbers are odd integers (1, 5, 9, ...) and the even-positioned numbers are negative odd integers (-3, -7, -11, ...).

To calculate the sum of the series, we can use the formula for the sum of an arithmetic series:

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

where n is the number of terms in the series.

The first term (a) is 1, and the last term (l) is 101.

Now, let's find the number of terms in the series (n):

To find the number of terms in an arithmetic series, we can use the formula:

n = (last term - first term) / common difference + 1

Since the common difference is 2 (difference between consecutive odd integers), we get:

n = (101 - 1) / 2 + 1 = 100 / 2 + 1 = 50 + 1 = 51

Now, we have n = 51. Let's calculate the sum:

Sum = (51/2) * (1 + 101) = 26 * 102 = 2652

The sum of the series 1-3+5-7+...-99+101 is 2652.