Use induction to prove that when $n≥1$, $a_i\in R$, $a_i > 0$, if $a_1a_2...a_n=1$, then $(1+a_1)(1+a_2)...(1+a_n)≥2^n$
Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$