Tính A

To find the sum of the arithmetic series A = -1 - 3 - 5 - 7 - ... - 2023, we can use the formula for the sum of an arithmetic series:

Sn = (n/2)(a1 + an)

where Sn is the sum of the series, n is the number of terms, a1 is the first term, and an is the last term.

In this case, the first term a1 = -1 and the last term an = -2023. We need to find the number of terms, n.

The common difference d between consecutive terms in this series is -2 (each term is obtained by subtracting 2 from the previous term).

To find n, we can use the formula for the nth term of an arithmetic series:

an = a1 + (n-1)d

Substituting the values, we have:

-2023 = -1 + (n-1)(-2)

Simplifying:

-2023 = -1 - 2n + 2

-2023 = 1 - 2n

-2024 = -2n

n = -2024 / -2

n = 1012

Now that we know n, we can find the sum Sn:

Sn = (n/2)(a1 + an)

Sn = (1012/2)(-1 + (-2023))

Sn = 506(-1 - 2023)

Sn = 506(-2024)

Sn = -1,025,504

Therefore, the sum of the arithmetic series A = -1 - 3 - 5 - 7 - ... - 2023 is -1,025,504.