Let this number be x. Then its reciprocal is 1/x. And the sum of them is x+1/x.
In order to find the least possible sum, we can derivate the sum and set it to zero.
Derivation of x+1/x gives us, [tex]1- x^{-2} [/tex]. Setting it to zero, we are going to solve the following equation: [tex]1- \frac{1}{ x^{2} } =0[/tex]
And solving it, we obtain x=1 and x=-1. Since we were looking for a positive number, the answer is 1
