The sum of 1..n is n(n+1)/2. A. The sum of 1..N is N(N+1)/2. B. The sum of n..N = B-A. We want solutions to A = B-A. Or, 1 = B-A/A I leave the rest as

The sum of 1..n is n(n+1)/2. A. The sum of 1..N is N(N+1)/2. B. The sum of n..N = B-A. We want solutions to A = B-A. Or, 1 = B-A/A I leave the rest as an exercise for the reader. :)