Note:Level of difficulty:the lowest is $\displaystyle \star$ and the highest is $\displaystyle \star \star \star \star \star$. Have Fun!

$\displaystyle \star \star$Problem 1: Let $\displaystyle a_n=n\ln \left(1 + \frac{1}{n} \right), \ n \in \mathbb{N}.$ Evaluate $\displaystyle \left \lfloor \frac{a_n}{1-a_n} \right \rfloor.$