I Summation Equality

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1. Feb 7, 2017

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!

2. Feb 7, 2017

Dragon27

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

3. Feb 7, 2017

jenny_shoars

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!

4. Feb 7, 2017

Staff: Mentor

No.

Good suggestion.

5. Feb 7, 2017

Stephen Tashi

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

6. Feb 8, 2017

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.