Question 116
The multiplicative content of a set is the product of its elements. If the set has a single element, its multiplicative content is that single element and, if the set is empty, its multiplicative content is $1$. For example, the multiplicative content of $\{1,2,3\}$ is $1 \cdot 2 \cdot 3=6$.
a) Determine the sum of the multiplicative contents of all subsets of $\{1,2,3,4\}$.
b) Determine the sum of the multiplicative contents of all subsets of
$$
\left\{1, \frac{1}{2}, \frac{1}{3}, \ldots, \frac{1}{2016}\right\}
$$
a) Determine the sum of the multiplicative contents of all subsets of $\{1,2,3,4\}$.
b) Determine the sum of the multiplicative contents of all subsets of
$$
\left\{1, \frac{1}{2}, \frac{1}{3}, \ldots, \frac{1}{2016}\right\}
$$