I want to find the rate of convergence of

lim as n goes to infinity of (ln(n+1) - ln(n)), which equals

lim as n goes to infinity of ln((n+1)/n)

I said that ln[(n+1)/n) must be less than or equal to (n+n)/n^2 and it seems to work. Then, I think the rate if O(1/n).

However, I'm not sure how exactly to bound the ln function. Can someone show me a bound or why this works?