# Percise defination of the limit of a sequence problem

1. Feb 12, 2008

### GNelson

1. The problem statement, all variables and given/known data

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

3. The attempt at a solution

A sequence has a limit 0 if for every $$\epsilon$$>0 there exists a number N such that for every n > N

|ln(n)/n-0|<$$\epsilon$$

Take $$\epsilon$$=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 $$\epsilon$$.

2. Feb 12, 2008

### end3r7

You can find any natural number, so just get an upper bound for ln(n).

For example, ln(n) < sqrt(n)