Best Approximation from Below to 1 as Sum of Minimal Number of Unit Fractions

Theorem

 * $\dfrac 1 2 + \dfrac 1 3 + \dfrac 1 7 + \dfrac 1 {43} = 1 - \dfrac 1 {1806}$

This is the best approximation from below to $1$ as the minimal sum of unit fractions.