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

Submitted by Atanu Chaudhuri on Sun, 28/07/2019 - 04:56

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...