E^(-x/(1-x)) is less than 1-x is less than e^(-x) for nonzero real x less than 1
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Theorem
The following formula holds for $x \in (0,1)$: $$\exp \left( -\dfrac{x}{1-x} \right) < 1-x < e^{-x},$$ where $\exp$ denotes the exponential.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions: 4.2.29
