KöMaL 2007 B4021

Prove that if each of the numbers $a_1$,$a_2$,...,$a_n$ is at least 1, then ($a_1$+1)($a_2$+1)$^. ...^.$($a_n$+1) \ge$2^{n-1}$($a_1$+$a_2$+...+$a_n$-$n$+2).