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.

Proof

This theorem requires a proof. In particular: It is not clear exactly what is being stated here. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

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