Hello, it is pretty obvious that the following limit is equal to zero:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]$Lim t \rightarrow \infty (\tmop{te}^{- t}) = 0$[/tex]

For example, for t=100 it is [tex]100*e^{-100}[/tex]

But how would you take this limit "rigorously"? I tried decomposing the function with a mclaurin series and [tex]te^-t[/tex] is equal to this series:

[tex]$\sum_{n = 1}^{\infty} \frac{(- 1)^{n + 1} t^n}{(n - 1) !}$[/tex]

How would I actually evaluate this series for t->infinity???? Or is this the wrong approach?

Also for a finite number of terms it appears that this series diverges...

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# Simple limit

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