Question 66
For every real numbers $x_1, \dots, x_n$, prove that
$$
\frac{x_1}{1+x_1^2} + \frac{x_2}{1+x_1^2+x_2^2} + \dots + \frac{x_n}{1+x_1^2+\dots+x_n^2} \lt \sqrt{n}.
$$
$$
\frac{x_1}{1+x_1^2} + \frac{x_2}{1+x_1^2+x_2^2} + \dots + \frac{x_n}{1+x_1^2+\dots+x_n^2} \lt \sqrt{n}.
$$