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.
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.
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
$\displaystyle \chi$ $\displaystyle \sigma$