- #1

GNelson

- 9

- 0

## Homework Statement

it is shown that lim n->Infinity of ln(n)/n=0

Find a natural number N such that

n> N -> |ln(n)/n - 0| < 1/10

## The Attempt at a Solution

A sequence has a limit 0 if for every [tex]\epsilon[/tex]>0 there exists a number N such that for every n > N

|ln(n)/n-0|<[tex]\epsilon[/tex]

Take [tex]\epsilon[/tex]=1/10, as ln(n)/n > 0 for any sufficently large n we have

ln(n)/n < 1/10.

so I choose N=10ln(n).

My problem starts here this is a function of a variable being sent to infinity I am not sure how exactly one solves for N that is purely a function of [tex]\epsilon[/tex].