Problems(1)
Given a subset of {1,2,...,n}, we define its alternating sum in the following way: we order the elements of the subset in descending order and, starting with the largest, we alternately add and subtract the successive numbers. For example, the alternating sum of the set {1,3,4,6,8} is 8−6+4−3+1=4. Determines the sum of the alternating sums of all subsets of {1,2,...,10} with an odd number of elements. number theoryalgebra