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

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## 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.

## Proof

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## Sources

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $43$