Why does n^(c/n) approach 1 as n approaches infinity?

[tolove]

My book is showing this as an intuitive step, but I'm not quite seeing the reasoning behind it.

n**(c/n) → 1 as n → ∞, for, I think, any positive c. But why?

 

[Dick]

My book is showing this as an intuitive step, but I'm not quite seeing the reasoning behind it.

n**(c/n) → 1 as n → ∞, for, I think, any positive c. But why?

Take the log and look at the limit of that. Use l'Hopital's rule, if it doesn't seem intuitive.

 

[tolove]

Take the log and look at the limit of that. Use l'Hopital's rule, if it doesn't seem intuitive.

Thank you very much. I was looking for things to cancel out, since it was written as if it was a basic arithmetic step, and kept backing into the same wall.