How can we check that a numerical series is convergent?

There are many methods to check it, but the the most useful is: By comparison: if we find a series whose terms are greater than the given ones which is known to be convergent (an armonic series for example), then our series will be convergent too. On the other hand, if we find a series whose terms are less than the given one which is known to be divergent, then our series will be divergent.