the ph has already explained the proof for this in a previous thread. Ill re explain it for you.
Arithmetic mean:
Geometric mean: [tex] GM(a_1,.....a_n) = \sqrt[n]{a_1,....,a_n}
Proof by induction:
without loss of generality we may resclae so that . If all the proof is trivial.
Thus assume atleast one and one . We assume . By inductive assumption we have
thus we have
we need to show
this would follow if BUT
,
prooving what you have writen
http://www.math.princeton.edu/mathla...eanGeoMean.pdf
thats the one. PH what do you think? is that wrong? have you got a link for the maximisation proof?