Tính tổng

To find the sum of the given series, we can group the positive and negative terms separately and then add them together.

Grouping the positive terms:
4 + 5 + 8 + 9 + ... + 2020 + 2021

This is an arithmetic series with a common difference of 1 and the last term being 2021. We can use the formula for the sum of an arithmetic series:

Sn = (n/2)(a + l)

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

In this case, n = (2021 - 4)/2 + 1 = 1010, a = 4, and l = 2021. Plugging these values into the formula:

Sum of positive terms = (1010/2)(4 + 2021) = 1010 * 2025 = 2,045,250

Grouping the negative terms:
-2 + (-3) + (-6) + (-7) + ... + (-2020) + (-2021) + (-2022)

This is also an arithmetic series with a common difference of -1 and the last term being -2022. Using the same formula as above:

n = (2022 - 2)/2 + 1 = 1011, a = -2, and l = -2022

Sum of negative terms = (1011/2)(-2 + (-2022)) = 1011 * (-1012) = -1,022,332

Finally, adding the sum of the positive terms and the sum of the negative terms:

Sum = Sum of positive terms + Sum of negative terms
= 2,045,250 + (-1,022,332)
= 1,022,918

Therefore, the sum of the given series is 1,022,918.