# Calculating sum of a series

• alias25
In summary, the conversation is about someone asking for help with a math problem involving calculating the sum of a given expression. They provide their progress so far and ask for advice on how to simplify the expression and solve the problem. The expert summarizes the problem and suggests simplifying the term and then summing it from 1 to n.

#### alias25

sorry isn't a physics question more to do with maths.

is it ok to post it here? I can't see to delete it, maybe some one will move it for me? to the maths section. thanksL:)

I have to calculate:

sum of (from r=1 to n): 1/3 (r^3 - (r-1)^3 -1)

so far I've done:

let n = 3

so

sum = 1/3 (n^3 - (n-1)^3 -1)

+1/3 ( (n-1)^3 - (n-2)^3 - 1)

+1/3 ( (n-2)^3 - (n-3)^3 -1)

looking at ^

(n-3)^3 = 0

the 1/3 can be factorised out, the -1's sums to -n

so: sum = 1/3 (n^3 -...-n) (1)

this inbetween thing I am finding tricky

i noticed theres...-2(n-1)^3 - 2(n-2)^3...etc, when n = any number.

i can put that as

sum(from r=1 to n-1) of: (n-r)^3

so into (1):

1/3 (n^3 -2(sum from r=1 to n-1 ofn-r)^3) -n)

^but i don't think that's what they are looking for.

any help will be appriciated,thank you.

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Is this what you need to find $$\sum_{r=1}^{n}\left(\frac{1}{3}\left({r^3 - (r-1)^3 - 1}\right)\right)$$?

If so, why not simplify the term that is to be summed, i.e., $\frac{1}{3}\left(r^3 - (r-1)^3 - 1\right)$ and then sum it from 1 to n?

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I understand that mathematics is a fundamental tool for solving problems in many scientific fields, including physics. While this may not be a physics-specific question, it is still a valid question that requires mathematical skills to solve. It is perfectly acceptable to post it here, and I'm sure someone from the community will be able to help you with your calculations. However, if you feel that your question would be better suited for the math section, you can always ask a moderator to move it for you. In the meantime, I would suggest breaking down the problem into smaller parts and using algebraic manipulations to simplify the expression. Good luck!

## 1. What is the formula for calculating the sum of a series?

The formula for calculating the sum of a series is Sn = a1 + a2 + a3 + ... + an, where Sn represents the sum of n terms, and a1, a2, a3, etc. represent the individual terms in the series.

## 2. How do I know when to stop adding terms in a series?

You can stop adding terms in a series when you reach the desired number of terms, or when the pattern of the series becomes clear and you can determine the sum without adding any more terms.

## 3. Can I use a calculator to calculate the sum of a series?

Yes, you can use a calculator to calculate the sum of a series. However, it is important to understand the formula and the concept behind it in order to verify the accuracy of the calculator's result.

## 4. Are there different types of series that can be summed?

Yes, there are different types of series that can be summed, such as arithmetic, geometric, and harmonic series. Each type has its own specific formula for calculating the sum.

## 5. What is the purpose of calculating the sum of a series?

The purpose of calculating the sum of a series is to determine the total value of a sequence of numbers. This can be useful in various mathematical and scientific applications, such as finding the average, predicting future values, and analyzing data.