Difference between revisions of "1+x greater than exp(x/(1+x)) for nonzero real x greater than -1"
From specialfunctionswiki
(Created page with "==Theorem== The following formula holds for nonzero $x \in \mathbb{R}$ with $x>-1$: $$1+x > \exp \left( \dfrac{x}{1+x} \right),$$ where $\exp$ denotes the exponential. ==...") |
|||
| (3 intermediate revisions by the same user not shown) | |||
| Line 7: | Line 7: | ||
==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=X less than e^x-1 less than x/(1-x) for nonzero real x less than 1|next=}}: 4.2.34 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=X less than e^x-1 less than x/(1-x) for nonzero real x less than 1|next=e^x greater than 1+x^n/n! for n greater than 0 and nonzero real x greater than 0}}: $4.2.34$ |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 00:34, 23 December 2016
Theorem
The following formula holds for nonzero $x \in \mathbb{R}$ with $x>-1$: $$1+x > \exp \left( \dfrac{x}{1+x} \right),$$ where $\exp$ denotes the exponential.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.2.34$
