In 1985, graphic novelist Alison Bechdel came up with criteria for whether she'd watch a movie. It's become known as the Bechdel test, and it's surprisingly hard for films to pass these days. After ...

Given a decreasing sequence {aⁿ} of nonnegative terms, we prove that there exist subsequences {nk } of {n} such that ∑k=1∞nk+1−nkank and ∑n=1∞an have the same convergence. In particular, ∑n=1∞an ...