If there is a given series $\sum_{i=0}^∞ b_n$ that diverges, how would the infinite sum of $a_{4n}$ behave differently, and what would be a method to compare the two series to test convergence of the latter?
I understand that if $a_{n}$ is decreasing, $a_{(4n)}$ would approach $0$ quicker and therefore be more likely to converge, but I'm not sure how to test for/prove that.
-thanks