# Thread: Calculus: Art Of Problem Solving (1)

1. ## Calculus: Art Of Problem Solving (1)

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 $\displaystyle \left \lfloor \frac{a_n}{1-a_n} \right \rfloor.$

2. Originally Posted by NonCommAlg
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 $\displaystyle \left \lfloor \frac{a_n}{1-a_n} \right \rfloor.$
Wait, is it still a limit? You had a limit, are you using the conveniton that a non-descript limit should be taken as going to infinity?

3. Originally Posted by Mathstud28
Wait, is it still a limit? You had a limit, are you using the conveniton that a non-descript limit should be taken as going to infinity?
no, it's not a limit. (i changed the problem because that was too easy!)