Question 192
Given $n$ positive real numbers $a_{1}, a_{2}, \ldots, a_{n}$ such that $a_{1} a_{2} \cdots a_{n}=1$, prove that
$$
\left(1+a_{1}\right)\left(1+a_{2}\right) \cdots\left(1+a_{n}\right) \geq 2^{n}
$$
When does the equality hold?
$$
\left(1+a_{1}\right)\left(1+a_{2}\right) \cdots\left(1+a_{n}\right) \geq 2^{n}
$$
When does the equality hold?