pure Gn≦An

(a) prove that lnx ≦ x-1 for all x >0
When does the equality holds?
(b) Let a1, a2, a3, ... , an be n positive real numbers
Define An = 1/n ε(i=1 → n) ai
Gn = [Π (i=1 → n) ai ]^(1/n)
show that Gn≦An when does the equality hold?