Assume n=2. Then we have 2-1 = 1 on the left side and 2*1/2 = 1 on the right side.
Denote f(n) = (n-1)+(n-2)+(n-3)+...+1
Now assume we have tested up to n=k. Then we have to test for n=k+1.
on the left side we have k+(k-1)+(k-2)+...+1, so it's f(k)+k
On the right side we then have (k+1)*k/2 = (k^2+k)/2 = (k^2 +2k - k)/2 = k+(k-1)k/2 = kf(k)
So this have to hold for every k, and this concludes the proof.
