Prove by induction on m, The quantities ai in this exercise

Prove by induction on m

Reference no: EM13963109

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 ··· a_p ≤(a1 + a2 + ··· + a_p/p)^p,

where p = 2^m with m a positive integer. Note that each increase of m by unity doubles the number of factors in the product.

Reference no: EM13963109

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