# Summation Equality: Is it Me or Author?

• I
• jenny_shoars
In summary, the conversation revolves around an equation that the author claims to be incorrect. The equation is about the sum of terms and the author is having trouble understanding it. Another person suggests expanding the square, but the author has already tried that. The author eventually realizes their mistake and it is just a simple error on their part.
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!

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.

## 1. What is summation equality?

Summation equality is a mathematical concept that states that the sum of two or more quantities is equal to the sum of their individual parts. In other words, the total amount is the same regardless of how the quantities are grouped or ordered.

## 2. How is summation equality used in science?

In science, summation equality is often used to simplify complex equations or expressions. It allows scientists to break down a problem into smaller parts and then combine the results to find the overall solution. This is particularly useful in fields such as physics and chemistry where there are many variables and equations to consider.

## 3. Is summation equality always true?

Yes, summation equality is a fundamental property of mathematics and is always true. It is a basic principle that is used in many mathematical proofs and is a key concept in calculus and other branches of mathematics.

## 4. How is summation equality different from the distributive property?

While both concepts involve the combining of multiple quantities, the distributive property only applies to multiplication and division. Summation equality, on the other hand, applies to addition and subtraction. Additionally, the distributive property allows for the factoring out of a common factor, while summation equality is concerned with the total sum of all the quantities.

## 5. Can summation equality be applied to any type of numbers?

Yes, summation equality can be applied to any type of numbers, including whole numbers, fractions, decimals, and even complex numbers. It is a universal concept in mathematics and has applications in many different fields, including science, finance, and engineering.

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