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There is
 alternating series test, and
 ``absolute convergence implies convergence''
So in the rare cases that you can't use the alternating series test,
use any of the tests for positive series for
.
If the problem also asks about convergence and absolute convergence,
always consider the sequence
separately.
Which of the following series converge? Which of them converge absolutely?




(The last one is a bit more tricky than the others.)
Arend Bayer
20061215