Question 1
Let $x_1,x_2,\ldots,x_n$ be positive real numbers, and let $S=x_1+x_2+\cdots+x_n$. Prove that
$$(1+x_1)(1+x_2)\cdots(1+x_n)\le 1+S+\frac{S^2}{2!}+\frac{S^3}{3!}+\cdots+\frac{S^n}{n!}.$$
$$(1+x_1)(1+x_2)\cdots(1+x_n)\le 1+S+\frac{S^2}{2!}+\frac{S^3}{3!}+\cdots+\frac{S^n}{n!}.$$