Question 16
If
$$
\frac{x_1}{x_1 + 1} = \frac{x_2}{x_2 + 3} = \frac{x_3}{x_3 + 5} = \dots = \frac{x_{1006}}{x_{1006} + 2011},
$$
$$
x_1 + x_2 + \dots + x_{1006} = 503^2,
$$
determine $x_{1006}$.
$$
\frac{x_1}{x_1 + 1} = \frac{x_2}{x_2 + 3} = \frac{x_3}{x_3 + 5} = \dots = \frac{x_{1006}}{x_{1006} + 2011},
$$
$$
x_1 + x_2 + \dots + x_{1006} = 503^2,
$$
determine $x_{1006}$.