Question 2
Let $x_{1}, x_{2}, \ldots, x_{n}$ be positive real numbers, and let
$$
S = x_{1} + x_{2} + \cdots + x_{n} .
$$
Prove that
$$
\left(1 + x_{1}\right)\left(1 + x_{2}\right) \cdots \left(1 + x_{n}\right) \leq 1 + S + \frac{S^{2}}{2!} + \frac{S^{3}}{3!} + \cdots + \frac{S^{n}}{n!} .
$$
$$
S = x_{1} + x_{2} + \cdots + x_{n} .
$$
Prove that
$$
\left(1 + x_{1}\right)\left(1 + x_{2}\right) \cdots \left(1 + x_{n}\right) \leq 1 + S + \frac{S^{2}}{2!} + \frac{S^{3}}{3!} + \cdots + \frac{S^{n}}{n!} .
$$