Let's assume that every a belongs to real numbers set and s is a sum of all the numbers from $a_1, a_2...a_n$. How would you prove this?
$\frac{a_1}{s - a_1}$ + $\frac{a_2}{s - a_2}$ ...+$\frac{a_n}{s - a_n}\ge \frac{n}{n - 1}$
Comparing a sequence of fractions with a fraction
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sequences-and-series
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0Can you prove it for two numbers? How about three? What else have you tried? – 2017-02-27
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0are the variables assumed to be positive? – 2017-02-27
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0Yes, they should be positive, I apologize for not mentioning it! – 2017-02-27
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0The question is answered differently here: [Proof for an inequality problem using the rearrangement inequality](http://math.stackexchange.com/questions/1910308/proof-for-an-inequality-problem-using-the-rearrangement-inequality) – 2017-03-01