# Summation Notation for [(i^3)/(N^3)]

• Lo.Lee.Ta.
In summary, the conversation is about summation notation and how to find the value of a summation with a variable in the denominator. The person is confused about how to add something N times and asks for help. The expert suggests using an ellipsis to expand the summation and provides an example of the expanded form. The person asks for confirmation on their answer and the expert confirms it. They also mention that there is a formula for finding the value of the summation and suggest looking it up.
Lo.Lee.Ta.
I think I get summation notation when when there are more numbers than variables
6
Ʃ i/6 <---I can figure that out.
i=1

But I'm confused on how to find what this equals:
N
Ʃ (i^3)/(N^3) = ?
i=1

How do you add something N times? ...I could deal with a number like 6, but I'm confused about N...

Any help? :/

Thank you! :)

Lo.Lee.Ta. said:
I think I get summation notation when when there are more numbers than variables
6
Ʃ i/6 <---I can figure that out.
i=1

But I'm confused on how to find what this equals:
N
Ʃ (i^3)/(N^3) = ?
i=1

How do you add something N times? ...I could deal with a number like 6, but I'm confused about N...

Any help? :/

Thank you! :)

The first term in the summation is 1/N3.
The second term is 8/N3.

Can you continue?
What is the last term in the summation?

You will necessarily need to use an ellipsis (i.e., "..." ) when you expand this summation.

So the (N)^3 in denominator is just kept as (N)^3!

Okay, would this be the answer then:

1/(N^3) + 8/(N^3) + 27/(N^3) + ... + ((N-1)^3)/(N^3) + (N^3)/(N^3)

Lo.Lee.Ta. said:
So the (N)^3 in denominator is just kept as (N)^3!

Okay, would this be the answer then:

1/(N^3) + 8/(N^3) + 27/(N^3) + ... + ((N-1)^3)/(N^3) + (N^3)/(N^3)

Yes, if that's the form you want the answer in. If you actually want to sum it up there is a formula for 1^3+2^3+3^3+...+N^3. Just like there is a formula for 1+2+3+...+N=(N+1)N/2. Probably easiest to try and look it up unless you are required to prove it.

## 1. What is Summation Notation for [(i^3)/(N^3)]?

Summation notation is a way to represent a series of numbers or terms in a compact form. In the expression [(i^3)/(N^3)], "i" represents the index or variable that changes with each term in the series, and "N" is the upper limit or the number of terms in the series. The superscript "3" indicates that each term is cubed.

## 2. How do you calculate the value of [(i^3)/(N^3)] using Summation Notation?

To calculate the value of [(i^3)/(N^3)] using summation notation, you need to plug in the values of "i" and "N" into the expression and then add up all the terms. For example, if i ranges from 1 to 5, the expression would be [(1^3)/(5^3)] + [(2^3)/(5^3)] + [(3^3)/(5^3)] + [(4^3)/(5^3)] + [(5^3)/(5^3)], which simplifies to 0.488.

## 3. What is the purpose of using Summation Notation for [(i^3)/(N^3)]?

Summation notation is used to simplify and generalize mathematical expressions. It allows us to represent a series of numbers or terms in a compact form, making it easier to work with and understand complex mathematical concepts and formulas.

## 4. Can Summation Notation be used for other types of series or expressions?

Yes, summation notation can be used for various types of series, including arithmetic, geometric, and harmonic series. It can also be used for other types of expressions, such as polynomials and trigonometric functions.

## 5. What are some applications of Summation Notation for [(i^3)/(N^3)]?

Summation notation is commonly used in mathematics, statistics, and other scientific fields to represent and solve various types of problems and equations. It can also be applied in computer programming and data analysis to perform calculations and manipulate large sets of data efficiently.

Replies
16
Views
2K
Replies
3
Views
1K
Replies
5
Views
1K
Replies
17
Views
2K
Replies
6
Views
1K
Replies
7
Views
843
Replies
3
Views
1K
Replies
18
Views
2K
Replies
8
Views
2K
Replies
3
Views
2K