# Summation Equality

## Main Question or Discussion Point

I'm doing my first paper review and an equation is holding me up. I can't tell if I'm just missing something silly or if the author made a mistake.

Given that:
$$\sum_{n=1}^{N}s_{n} = 1$$
The author says that:
$$\sum_{n=1}^{N}(s_{n} - \frac{1}{N})^{2} = \sum_{n=1}^{N}s_{n}^{2} - \frac{1}{N}$$
I seem to be having some trouble getting this to work. Am I just missing something? Or is this the author's mistake? Thanks!

I seem to be having some trouble getting this to work.
Seems fine to me. Have you tried expanding the square or anything?

Seems fine to me. Have you tried expanding the square or anything?
I did, but still didn't seem to get it to come out right. But, now that I know it's just me, I'll figure it out. Thanks!

Mark44
Mentor
Or is this the author's mistake?
No.

Have you tried expanding the square or anything?
Good suggestion.

Stephen Tashi
Keep in mind that for a constant term $k$ , $\sum_{k=1}^N k = Nk$.
Sorry, I discovered my error very shortly after reading Dragon27's reply. I had made a very simple mistake where I wrote $$\frac{N}{N^2}=N$$. Just not enough sleep I guess.