Question

How do you find the Limit of `ln(n+1) - ln(n)` as n approaches infinity?

Answer 1

Use `lna-lnb=ln(a/b)` and continuity of `ln`.

Explanation:

`lim_(nrarr00)(ln(n+1)-ln(n) = lim_(nrarroo)ln((n+1)/n)`

`= ln(lim_(nrarroo)(n+1)/n)`

`= ln(1) = 0`

Note that

`lim_(nrarroo)(n+1)/n = lim_(nrarroo)(canceln(1+1/n))/(canceln*1)`

`= (1+0)/1=1`