15. Given the set $A=\{1,2,3, \cdots, 2019\}$, for each non-empty subset of set $A$, calculate the reciprocal of the product of all its elements. Then the sum of all these reciprocals is
The answer is $(1+1)\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right) \cdots\left(1+\frac{1}{2019}\right)-1=2020-1=2019$. Note: In this problem, $1, \frac{1}{2}, \frac{1}{3}, \cdots, \frac{1}{2019}, \frac{1}{1 \times 2}, \frac{1}{1 \times 3}, \cdots, \frac{1}{1 \times 2019}$ are different.