- #1
henry wang
- 30
- 0
Is ∑f from a to b the same as ∑f from b to a?
In other words, does the order of summation matter?
In other words, does the order of summation matter?
Thank you.BvU said:No, since a+b = b+a
Thank you.zinq said:I'll add that, if there is only a finite number of terms, or if all but finitely many nonzero terms are of the same sign, then any order of summation gives the same result.
But (and I hope this is not too much information):
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For any convergent infinite summation
∑ cj = K
that does not converge absolutely:
∑ |cj| = ∞,
then there is an surprising theorem that suggests how important it is to be cautious:
Theorem: For such a summation as ∑ cj, and any real number L, there is some rearrangement ∑' of the order of summation such that
∑' cj = L.
henry wang said:Thank you.
In post #1 there is.zinq said:if there is only a finite number of terms
Reversing the order of summation refers to changing the order in which mathematical operations are performed in a series. In summation, this means changing the order in which terms are added together.
Reversing the order of summation can be useful for simplifying complicated series or for solving problems that cannot be solved using the original order. It can also help to identify patterns or relationships between terms.
The steps to reverse the order of summation involve changing the index of summation, or the variable used to represent the terms in the series. This can be done by replacing the original index with a new variable and then solving for the original index in terms of the new variable.
No, it is not always possible to reverse the order of summation. This depends on the specific series and the relationship between its terms. In some cases, reversing the order may not lead to a simpler or solvable solution.
Reversing the order of summation can be applied in various fields of science and engineering, such as physics, mathematics, and computer science. It can be used to solve problems involving sequences, series, and probabilities, and to analyze data in a different way. It can also be used in optimization and algorithm design.