Question

A set S=[1,2........n],if X is a subset of S, we call the sum of X's elements the VOLUME of X if the volume of X is odd(or even) number so we call X the odd(even)subset of S,demonstrate that the number of odd subsets and even subsets of S are equal

Answer 1

this is my opinion let y=[1,2......n] ,so the biggest volume is(1+n)n/2 so i think i just need to prove that the the number of odd number and even number of set N=[1,2,3......(1+n)n/2] are equal is that right??? :D