To find the sum of the given series, we can group the terms in pairs:

(-21 + 22) + (-23 + 24) + ... + (-2021 + 2022)

Each pair of terms has a sum of 1:

1 + 1 + ... + 1

The number of pairs is equal to half the number of terms in the series. Since the series goes from -21 to 2022, there are (2022 - (-21) + 1) = 2044 terms. Therefore, there are 2044/2 = 1022 pairs.

So, the sum of the series is 1 * 1022 = 1022.