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

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

Transcribed Image Text:

1 1 In 2. 2 3 4 1 |1 + 3 3 In 2. 1 1 7. ||