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

S2 = (2-4) + (6+8) + (10-12) + (14+16) + ... + (1994-1996) + (1998+2000)

Now, let's simplify each pair:

S2 = -2 + 14 + -2 + 30 + ... + -2 + 3998

We can see that the series consists of pairs of -2 and increasing even numbers. The number of pairs can be found by dividing the difference between the first and last term by the common difference and adding 1:

Number of pairs = (2000 - 2) / 4 + 1 = 500

Now, we can calculate the sum of the pairs:

Sum of pairs = -2 * 500 = -1000

Therefore, the sum of the given series S2 is -1000.