Question 20
Given a positive integer number $n$, determine the minimum of
$$
\max \left\{ \frac{x_1}{1+x_1}, \frac{x_2}{1+x_1+x_2}, \dots, \frac{x_n}{1+x_1+x_2+\dots+x_n} \right\},
$$
as $x_1, x_2, \dots, x_n$ run through all non-negative real numbers which add up to 1.
$$
\max \left\{ \frac{x_1}{1+x_1}, \frac{x_2}{1+x_1+x_2}, \dots, \frac{x_n}{1+x_1+x_2+\dots+x_n} \right\},
$$
as $x_1, x_2, \dots, x_n$ run through all non-negative real numbers which add up to 1.