This question in itself isn't the tough part; its the series we're given that's really strange.
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Investigate the convergence (absolute and conditional) for the series u_n given by
1/(ln2) - 1/(2ln3) - 1/(2ln4) + 1/(2²ln5) + 1/(2²ln6) + 1/(2²ln7) + 1/(2²ln8) - 1/(2³ln9) - ...
- 1/(2³ln16)...
