Question 17
$x_1$, $x_2$, ..., $x_n$ are positive reals with sum $1$. Let $s$ be the largest of $\dfrac{x_1}{1 + x_1}$, $\dfrac{x_2}{1 + x_1 + x_2}$, ..., $\dfrac{x_n}{1 + x_1 + ... + x_n}$. What is the smallest possible value of $s$? What are the corresponding $x_i$?