I am trying to prove that some particular infinite series is Cauchy. Of course, I know what it means for a sequence to be Cauchy, but I can't seem to find anything related to Cauchy series. Could someone help me to interpret the meaning of this?
Maybe it means that the sequence of partial sums is Cauchy?
As you assumed, a series is Cauchy if the sequence of its partial sums is a Cauchy sequence.