How does one prove that the series

1 + 1/3 - 1/2 + 1/5 + 1/7 - 1/4 + 1/9 + 1/11 - 1/6 + ...

converge?

PS.: This series is a rearrangement of the alternating harmonic series in which two positive terms are always followed by one negative.

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- Nov 25th 2010, 06:57 PMjefferson_lcconvergence of series.
How does one prove that the series

1 + 1/3 - 1/2 + 1/5 + 1/7 - 1/4 + 1/9 + 1/11 - 1/6 + ...

converge?

PS.: This series is a rearrangement of the alternating harmonic series in which two positive terms are always followed by one negative. - Nov 25th 2010, 07:39 PMchisigma
The series converges... but not as $\displaystyle \displaystyle 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + ... = \ln 2$ because that is a

*weakly convergent series*...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - Nov 26th 2010, 04:21 AMtonio