MathDB

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\}

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.

Problem Statement