Kummer test and regular variation

A new test for convergence of positive series

“…The main point of the next theorem is that it not only provides a condition to conclude convergence or divergence, but also gives information about the rate at which this happens. This result is also available in [14].…”

“…This simple test can be extended and leads to a new test based on logarithms. The same framework has been used by Řehák [13,14] to extend the formula of Raabe. We show how the new definitions lead to new convergence/divergence tests.…”