To simplify this expression, we need to first evaluate each term individually and then sum them up.

3/2^2 = 3/4 = 0.75
8/3^2 = 8/9 ≈ 0.8889
...
2023^2-1/2023^2 = 2023^2 - 1/2023^2

Now, we need to calculate the sum of these terms:

0.75 + 0.8889 + ... + (2023^2 - 1/2023^2)

To calculate the sum, we need to evaluate the last term and then add up all the terms:

2023^2 - 1/2023^2 = 4084129 - 1/4084129 ≈ 4084128.9999999998

Now, we add up all the terms:

0.75 + 0.8889 + ... + 4084128.9999999998

The sum of these terms is approximately 4084132.6389.