The quantities ai in this exercise are all positive real numbers.
(a) Show that a1a2 ≤(a1 + a2/2) 2.
(b) Hence, prove by induction on m that
a1a2 ··· ap ≤(a1 + a2 + ··· + ap/p) p,
where p = 2m with m a positive integer. Note that each increase of m by unity doubles the number of factors in the product.