My solution: Write the even integers between 1 and n (where n is odd ) in two rows with opposite order: ASCENDING ORDER: 2, 4, 6,..., (n-5), (n-3),(n-1) DESCENDING ORDER: (n-1), (n-3), (n -5)..., 6, 4 , 2 Summing each term in the two rows gives: (n+1) + (n+1) .... + (n+1) = (n-1)*(n-1)/2 (since ther...