## Average of Fractions

version = 1.01 of avfrac.tex 2014 Jan 19

https://alum.mit.edu/www/toms/
Suppose we have n positive numbers, x_{1}, x_{2}, …x_{n}.

We find the sum:

| (1) |

If S > 0 we can formulate n fractions:

What is the average of the fractions? No matter what the distribution of n fractions is, their average is always 1∕n!