  Translation of "Methodus succincta summas serierum infinitarum per formulas
differentiales investigandi" (1780). Euler wants to represent some given series
of functions S(x)=X(x)+X(x+1)+X(x+2)+etc. in a different way. He writes S as a
series in derivatives of X with unknown coefficients. He makes a generating
function V(z) out of these coefficients, which is the same as a generating
function that involves the Bernoulli numbers.

History and Overview;Classical Analysis and ODEs