Summation Equality: Is it Me or Author?

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Discussion Overview

The discussion revolves around a mathematical equation related to summation and variance, specifically examining whether a participant has misunderstood the equation or if there is an error in the author's formulation. The scope includes mathematical reasoning and problem-solving in the context of reviewing a paper.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • A participant questions the validity of an equation presented in a paper, specifically whether the equation holds true given the condition of the summation.
  • Another participant suggests expanding the square as a method to resolve the confusion.
  • The original poster expresses difficulty in obtaining the correct result even after attempting the suggested method.
  • A later reply indicates that the original poster discovered a simple error in their calculations, attributing it to lack of sleep.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the author's equation initially, but the original poster later acknowledges their own mistake, suggesting a resolution to their confusion.

Contextual Notes

The discussion reflects a reliance on specific mathematical manipulations and assumptions about summation properties, with an emphasis on the importance of careful calculation in mathematical proofs.

jenny_shoars
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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!
 
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jenny_shoars said:
I seem to be having some trouble getting this to work.
Seems fine to me. Have you tried expanding the square or anything?
 
Dragon27 said:
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!
 
jenny_shoars said:
Or is this the author's mistake?
No.

Dragon27 said:
Have you tried expanding the square or anything?
Good suggestion.
 
jenny_shoars said:
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##.
 
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.
 

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