"e" as the limit of a binomial

* Raise [math]n[/math] to the maximum on the slider and observe how the red curve [math]g(x)=\left(1+\frac{R}{n}\right)^{nx}[/math] approaches the blue curve [math]f(x)=e^{Rx}[/math]. * Deduce an expression for [math]e[/math]. * How would the expression change if [math]R>2[/math]?

Note that [math]f(x) > g(x)[/math] for a given growth rate [math]R[/math] for all [math]x[/math].