Find the limit as n goes to infinity of ln(n) / n ?

Answer 1

ln(n)/n as n approaches infinity is 0.

Use L'Hopital's rule:
Take the derivative of the numerator "ln(n)" and you get 1/n.
Take the derivative of the denominator "n" and you get 1.

So the derivative of the fraction is 1/n. Plug in infinity into n, and you get 1/∞.

1/∞ = 0 can be explained by dividing 1 by a greater and greater number (1/10=.1, 1/100=.01, 1/1000=.001) and you will notice that the number gets smaller and smaller. At infinity, the number is 0.

I didn't know how much explanation was necessary or more than enough...but I hope this helps :)

Answer 2

This requires the use of L'Hopital's rule.

Since limit as n goes to infinity of ln(n)/n = infinity/infinity, you apply L'Hopital's rule (look it up in a textbook or something if you are not familiar with this rule) to obtain limit as n goes to infinity equals limit as n goes to infinity of (1/n) / 1 = 1/n = 0.

Problem solved.

Answer 3

This is in ∞/∞ form, so use L'Hopital's rule:
lim (n->∞) ln n / n
= lim (n->∞) (1/n) / 1
= 0.