The set is $\left\{\dfrac{n}{n+1} : n=1,2,3,\ldots\right\}$. As $n\to\infty$, $\dfrac{n}{n+1}\to 1$, but never equals $1$. The sequence is strictly increasing and bounded above by $1$. Since $1$ is the infimum of all upper bounds and is itself an upper bound (the sequence never reaches $1$), the least upper bound (supremum) is $\mathbf{1}$.