A counting problem

05082010, 04:32 PM
Post: #1




A counting problem
For any nonempty subset $A$ of $\{1, 2, \ldots , n\}$ define $f(A)$ as the largest element of $A$ minus the smallest element of $A$. Find $\sum f(A)$ where the sum is taken over all nonempty subsets of $\{1, 2, \ldots , n\}$.


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