sum of series depends on order
According to the Leibniz’ test (http://planetmath.org/LeibnizEstimateForAlternatingSeries), the alternating series
Then we add these two series termwise getting the sum
Hence, this last series exactly the same as the original, but its sum is fifty percent greater. This is possible because the original series is not absolutely convergent: the series which is formed of the absolute values of its is the divergent harmonic series.
P. S. – For justification of the used manipulations of the series, see the entry.
|Title||sum of series depends on order|
|Date of creation||2013-03-22 14:50:59|
|Last modified on||2013-03-22 14:50:59|
|Last modified by||pahio (2872)|