Riemann Series Theorem - Statement of The Theorem

Statement of The Theorem

Suppose that

is a sequence of real numbers, and that is conditionally convergent. Let be a real number. Then there exists a permutation of the sequence such that

There also exists a permutation such that

The sum can also be rearranged to diverge to or to fail to approach any limit, finite or infinite.

Read more about this topic:  Riemann Series Theorem

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