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**mremwo** The exercise is to show that the sequence $\displaystyle x^2$$\displaystyle e^{-nx}$ converges uniformly on $\displaystyle [0, \infty)$

I know that the sequence converges to 0 because $\displaystyle x^2$$\displaystyle e^{-nx}$ = $\displaystyle x^2$($\displaystyle e^{-x}$)^n and $\displaystyle e^{-x}$ is always less than 1.

It makes sense that it converges uniformly since $\displaystyle e^{-nx}$ will go to 0 as $\displaystyle n \rightarrow \infty$, not depending on what x is, but I don't know how to show this using the definition of uniform convergence. Help is appreciated. Thank you!