Summation Equality: Is it Me or Author?

[jenny_shoars]

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!

 

[Dragon27]

I seem to be having some trouble getting this to work.

Seems fine to me. Have you tried expanding the square or anything?

 

[jenny_shoars]

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]

Or is this the author's mistake?

No.

Have you tried expanding the square or anything?

Good suggestion.

 

[Stephen Tashi]

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!

Keep in mind that for a constant term $k$ , $\sum_{k=1}^N k = Nk$.

 

[jenny_shoars]

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.