Difference between revisions of "E^x greater than 1+x^n/n! for n greater than 0 and nonzero real x greater than 0"
From specialfunctionswiki
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=1+x greater than exp(x/(1+x)) for nonzero real x greater than -1|next=e^x greater than (1+x/y)^y greater than exp(xy/(x+y) for x greater than 0 and y greater than 0)}}: 4.2.35 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=1+x greater than exp(x/(1+x)) for nonzero real x greater than -1|next=e^x greater than (1+x/y)^y greater than exp(xy/(x+y) for x greater than 0 and y greater than 0)}}: $4.2.35$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 00:35, 23 December 2016
Theorem
The following formula holds for $n>0$ and nonzero $x \in \mathbb{R}$ with $x>0$: $$e^x > 1 + \dfrac{x^n}{n!},$$ where $e^x$ denotes the exponential.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.2.35$
