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Algebraic proof of Least value of sum of reciprocals for any number of positive variables


The result of the least value of sum of reciprocals, used in Algebra represents an important principle of value sharing.

For two positive real variables $a$ and $b$ for example, if $a+b=1$, the least value of sum of reciprocals of $a$ and $b$ will occur when the value of the sum 1 is shared equally between the two variables. This remarkable equal value sharing principle hold true for any number of variables as well as for any positive sum of the variables...


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