The series below includes the consecutive even integers from 2 to 2022 inclusive, where the signs of the terms alternate between positive and negative:

$$
S=2-4+6-8+10-\cdots-2016+2018-2020+2022
$$

What is the value of $S$ ?
The terms being added and subtracted are the integers 2(1), 2(2), 2(3), and so on up to 2(1011). This means there are 1011 terms in total, which is an odd number of terms.

We will now insert parentheses to group the terms in pairs starting with the first two terms, then the second two terms, and so on.

Since the total number of terms is odd, 2022 will not be grouped with another term:

$$
S=(2-4)+(6-8)+(10-12)+\cdots+(2014-2016)+(2018-2020)+2022
$$

Each of the parenthetical expressions is equal to -2 , and the number of parenthetical expressions is $\frac{1011-1}{2}=505$.

Therefore,

$$
S=505(-2)+2022=-1010+2022=1012
$$

ANSWER: 1012