Q:

Converge or Diverge?  Which test to use? 

Hi does this series converge or diverge?  We've learnt so many tests and it's all so confusing I don't know which one to use.  Can someone start it off for me please
ii)$\sum_{k=1}^{\infty}\ln \left( \frac{k+2}{k+1} \right)$

A:

Consider the partial sum $$S_N=\sum_{k=1}^N\ln\left(\frac{k+2}{k+1}\right)=\sum_{k=1}^N\left(\ln(k+2)-\ln(k+1)\right)$$

