This is a series of the form S = Σ(1/(2n)(2n+1)), where n goes from 1 to 2020.

To find the sum of this series, we can rewrite each term as 1/2 * (1/(n) - 1/(n+1)). This is because 1/(2n)(2n+1) = 1/2 * (1/n - 1/(n+1)).

Now, we can simplify the series:

S = 1/2 * (1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2020 - 1/2021)
S = 1/2 * (1 - 1/2021)
S = 1/2 * (2020/2021)
S = 1010/2021

Therefore, the sum of the series is 1010/2021.