E^x is less than 1/(1-x) for nonzero real x less than 1
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Theorem
The following formula holds for nonzero $x \in \mathbb{R}$ with $x<1$: $$e^x < \dfrac{1}{1-x},$$ where $e^x$ denotes the exponential function.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): 4.2.31
