The Spitfire Mk1’s eight .303 Browning machine guns were lethal when aligned correctly - and this convergence test shows why. Precision fire at set distances turned the Spitfire into a flying scalpel ...

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 ...