Evaluating $\lim_{n\to\infty}{n\left(\ln(n+2)-\ln n\right)}$ I am trying to find$$\lim_{n\to\infty}{n\left(\ln(n+2)-\ln n\right)}$$ 
But I can't figure out any good way to solve this. 
Is there a special theorem or method to solve such limits? 

Hint
$$\ln(n+2)-\ln(n) = \ln\bigg (\frac{n+2}{n}\bigg)$$
