One thought on “OMK training立浩问的Vol2:Algebra pg66 Ex8-16 解答”

Just pointing out that this is wrong: on the fourth-last line, we know that LHS >= RHS, but LHS >= 1 does not imply that RHS >= 1.

A simple way is to note that by AM-GM, 1+a_i >= 2\sqrt{a_i}. Since the product of the a_i is 1, multiplying everything together gives (1+a_1)…(1+a_n) >= 2^n * \sqrt{a_1…a_n}=2^n.

Just pointing out that this is wrong: on the fourth-last line, we know that LHS >= RHS, but LHS >= 1 does not imply that RHS >= 1.

A simple way is to note that by AM-GM, 1+a_i >= 2\sqrt{a_i}. Since the product of the a_i is 1, multiplying everything together gives (1+a_1)…(1+a_n) >= 2^n * \sqrt{a_1…a_n}=2^n.