High school mathematics competition questions
The subset of the set A {1, 2,3 ... 1 00} contains the 99th power of 2 of the element 1, which is obvious because no subset of 1 comes from the set {2,3 ... 1 00}. . . 100 appears for 2 99 times, so the sum of all sxs is (2 99) * (1+2+3+...+100) = 5050 () * 2 99.