Anjanan A.

All possible non-empty subsets are taken from the set of numbers $1,2,3, \ldots, n$. For each subset, the reciprocal of the product of all its numbers is taken. Find the sum of all such reciprocal values.
The desired sum will result after expanding the brackets in the expression $\left(1+\frac{1}{1}\right)(1+1 / 2)\left(1+\frac{1}{3}\right) \ldots\left(1+\frac{1}{n}\right)-1$, which is equal to $2 / 1 \cdot 3 / 2 \cdot 4 / 3 \cdot \ldots \cdot{ }^{n+1} / n-1=n+1-1=n$.

## Answer

n.