Inequality with fraction

Question

I have tried with some numbers and the following dependency is true. But I have no idea on how to prove it? Notice that, the maximal value of $\ell$ is $n$ and the values of $l$ can be $l=k+1, k+2, \ldots, n$. Thanks in advance!

$$ \frac{n}{n+1}\cdot\frac{l}{k}>1, l>k$$

Answer 1

Note that

$$ \frac{n}{n+1}\cdot\frac{l}{k}>\frac{n}{n+1}\cdot\frac{n}{n-1}=\frac{n^2}{n^2-1}>1$$