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): $43$
