It can be proved that if a series converges absolutely, then its terms may be summed in

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It can be proved that if a series converges absolutely, then its terms may be summed in any order without changing the value of the series. However, if a series converges conditionally, then the value of the series depends on the order of summation. For example, the (conditionally convergent) alternating harmonic series has the value

1 1 In 2. 2 3 4

Show that by rearranging the terms (so the sign pattern is + + -),

1 |1 + 3 3 In 2. 1 1 7. ||

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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