A number $\displaystyle n\ge1$ is given. For a non-empty subset $\displaystyle X$ of the set $\displaystyle \{1,2,...,n\}$, let $\displaystyle a,\ b$ denominate respectively the smallest and the greatest element of the set $\displaystyle X$ and let $\displaystyle f(x)=\frac{1}{n-(b-a)}$.

Determine, according to $\displaystyle n$, the sum of numbers $\displaystyle f(X)$ for all non-empty subsets $\displaystyle X$ of the set $\displaystyle \{1,2,...,n\}$

Could anyone help me with this? I don't even have a clue on how to approach this problem...