[[Linear Transformation|Linear]] Convergence is a category of [[Order of Convergence]] in which $\alpha=1$. Note that this does not mean the [[Series]] itself is [[Linear Transformation|Linear]], just that its [[Rate of Convergence]] is. $\huge \alpha\set{e^{-n}} = \lim_{ n \to \infty } \frac{\ln e^{-n-1}}{ \ln e^{-n} } = \lim_{ n \to \infty } -\frac{n+1}{n} = \boxed{1} $