In my calculus class, whenever we try to find a limit of a sequence as it approaches infinity and it turns out to be like: $1^{\infty}$. We have to end up using L'Hopital's rule. I don't understand why it has to be L'Hopitaled, can't you just take the limit as the sequence approach $99999$ and the answer would be $1^{99999} = 1$ and you are done?
Why do we have to L'Hopital then?
Answer
Consider the following: $(1+1/n)^n \to e,$ while $(1+1/n)^{n^2} \to \infty.$
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