Question

Evaluate, hard limit problem.

Answer 1

\[ \lim_{x \rightarrow \infty} abs(\frac{ 1 }{ x! })^{1/x}\]

Answer 2

@iPwnBunnies

Answer 3

The answer solution says that the answer is 0, but I want to know how to do it.

Answer 4

My first observation is that, as it stands right now as x approaches infinity, we seem to get \(0^0 \). Do you agree with this assessment?
To fix that, we might like to use L'Hôpital's rule. But to do that, we need to get it into a form like 0/0 or infinity/infinity, right? Are you familiar with this sort of approach, or L'Hôpital's at all?

Answer 5

I know l'hopitals but how do you get it to 0/0 or infinity/ infinity?

Answer 6

You may wish to introduce a logarithm.

Answer 7

Okay thanks I need help with another problem right now.