Difference between revisions of "E^x greater than (1+x/y)^y greater than exp(xy/(x+y) for x greater than 0 and y greater than 0)"

Latest revision as of 07:43, 16 June 2016

Theorem

The following formula holds for $x>0$ and $y>0$: $$\exp \left( x \right) > \left( 1 + \dfrac{x}{y} \right)^y > \exp \left( \dfrac{xy}{x+y} \right),$$ where $\exp$ denotes the exponential.

Proof

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.2.36