i'm reading shilov's "real and complex analysis". there is a problem to prove that for real positive x1,x2,...xn, if x1*x2*...*xn=1, then x1+x2+...xn >= n. I proved this for the case n = 2. it says use induction on this case to prove it for the nth case. but i just don't see it.(adsbygoogle = window.adsbygoogle || []).push({});

for n=2:

(a+1)^2 >= 0

a^2 + 2a + 1 >= 0

a^2 + 1 >= 2a

a + 1/a >= 2

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# If the product of n numbers is 1, their sum is >= n

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