Question 114
Compute the sum:
$$
\frac{1}{\left(\frac{1}{2022}\right)^2 + 1} + \frac{1}{\left(\frac{2}{2021}\right)^2 + 1} + \frac{1}{\left(\frac{3}{2020}\right)^2 + 1} + \dots + \frac{1}{\left(\frac{2021}{2}\right)^2 + 1} + \frac{1}{\left(\frac{2022}{1}\right)^2 + 1}
$$
$$
\frac{1}{\left(\frac{1}{2022}\right)^2 + 1} + \frac{1}{\left(\frac{2}{2021}\right)^2 + 1} + \frac{1}{\left(\frac{3}{2020}\right)^2 + 1} + \dots + \frac{1}{\left(\frac{2021}{2}\right)^2 + 1} + \frac{1}{\left(\frac{2022}{1}\right)^2 + 1}
$$