Question 27
Find the value of the expression
$$
\frac{1}{\left(\frac{1}{2019}\right)^2 + 1} + \frac{1}{\left(\frac{2}{2018}\right)^2 + 1} + \frac{1}{\left(\frac{3}{2017}\right)^2 + 1} + \dots + \frac{1}{\left(\frac{2018}{2}\right)^2 + 1} + \frac{1}{\left(\frac{2019}{1}\right)^2 + 1}
$$
$$
\frac{1}{\left(\frac{1}{2019}\right)^2 + 1} + \frac{1}{\left(\frac{2}{2018}\right)^2 + 1} + \frac{1}{\left(\frac{3}{2017}\right)^2 + 1} + \dots + \frac{1}{\left(\frac{2018}{2}\right)^2 + 1} + \frac{1}{\left(\frac{2019}{1}\right)^2 + 1}
$$