# Order of summation in series with multiple indices

• I
• user15197573
In summary, the conversation discusses the necessity of absolute convergence in a special case of Fubini's theorem, also known as the "Re-ordering Theorem" or Mertens's theorem. An example is given to illustrate why absolute convergence is necessary. The original poster has found the answer to their question and will consider posting it in the future for the benefit of others.
user15197573
TL;DR Summary
Series property
Can someone help me understand why what I wrote is correct? That is: If I have a sequence with double indices and if the summation of the elements modules of this sequence converges (less than infinite) than it does not matter how I make this sum (second line) they are going to be always the same. Thank you.
edit: Guys, I've just found the answer to this question in another post but I don't know how to delete this.

Last edited:
Why not post the answer you found for the benefit of others who may find your post and who may have the same question. This would also allow us to comment on how good an answer it was and perhaps give you some deeper insight to your question.

user15197573
Sounds like a special case of Fubini's theorem to me.

user15197573
user15197573
jedishrfu said:
Why not post the answer you found for the benefit of others who may find your post and who may have the same question. This would also allow us to comment on how good an answer it was and perhaps give you some deeper insight to your question.
I'll take that into consideration in my next post since some people already answered here. Thank you.

## 1. What is the order of summation in a series with multiple indices?

The order of summation in a series with multiple indices refers to the specific sequence in which the terms of the series are added together. This is important because changing the order of summation can result in different values for the series.

## 2. How do you determine the order of summation in a series with multiple indices?

The order of summation is typically determined by the indices of the series. These indices indicate the specific variables that are being summed over. The order of summation is determined by the order in which these indices are written in the series.

## 3. What are the potential consequences of changing the order of summation in a series with multiple indices?

Changing the order of summation in a series with multiple indices can result in a different value for the series. This is because the terms of the series are being added in a different sequence, which can lead to different combinations and results. It is important to carefully consider the order of summation to ensure accurate calculations.

## 4. Can the order of summation in a series with multiple indices be changed?

Yes, the order of summation in a series with multiple indices can be changed. However, it is important to note that changing the order of summation can result in different values for the series. It is important to carefully consider the order of summation and its potential consequences before making any changes.

## 5. Are there any rules or guidelines for determining the order of summation in a series with multiple indices?

Yes, there are some rules and guidelines that can be followed when determining the order of summation in a series with multiple indices. These include the commutative and associative properties of addition, as well as considering the convergence of the series. It is also helpful to carefully examine the indices and consider the potential consequences of changing the order of summation.

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