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- Thread starter Austin
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- #2

Mark44

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The series 1 - 1/2 + 1/3 - 1/4 +- ... +(-1)

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pwsnafu

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I know when a series is conditionally convergent and I understand that being conditionally convergent means that rearrangement of the terms will not always lead to the same sum, but I am unsure why exactly this is important?

The most important aspect is that it is counter intuitive. Finite addition is commutative ##x+y=y+x##. Conditionally convergent series are not, so this is an example of a property which is true finitely but not infinitely.

Note that "will not always lead to the same sum" isn't the impressive aspect.

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