# Is $\sum(a-b)$ the same as $-\sum(b-a)$?

I am running through some numbers and found a mistake. Turns out I had to do $$\sum(b-a)$$ instead of $$\sum(a-b)$$. But, I only have the end result (I do not have a source data anymore).

Can just flip the sign of the end result?

Or, is $$\sum(b-a)$$ equal to $$-\sum(a-b)$$ ?

• Note that $$\sum\limits_i (a_i-b_i)=(a_1-b_1)+(a_2-b_2)+\cdots=-(b_1-a_1)-(b_2-a_2)-\cdots=-\sum\limits_i (b_i-a_i)$$ – TheSimpliFire Apr 9 at 9:43