- #1

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Is

In other words, does the order of summation matter?

**∑f**from**a to b**the same as**∑f**from**b to a**?In other words, does the order of summation matter?

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- Thread starter henry wang
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- #1

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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?

- #2

BvU

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No, since a+b = b+a

- #3

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Thank you.No, since a+b = b+a

- #4

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But (and I hope this is not too much information):

-----------------------------------------------------------

For any convergent infinite summation

∑ c

that does not converge absolutely:

∑ |c_{j}| = ∞,

then there is an surprising theorem that suggests how important it is to be cautious:

∑' c

- #5

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Thank you.

But (and I hope this is not too much information):

-----------------------------------------------------------

For any convergent infinite summation

∑ c_{j}= K

that does not converge absolutely:

∑ |c_{j}| = ∞,

then there is an surprising theorem that suggests how important it is to be cautious:

Theorem: For such a summation as ∑ c_{j}, and any real number L, there is some rearrangement ∑' of the order of summation such that

∑' c_{j}= L.

- #6

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- #7

BvU

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In post #1 there is.if there is only a finite number of terms

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