标题： 通过微分公式研究无穷级数和的简明方法 显示英文标题

标题： A succinct method for investigating the sums of infinite series through differential formulae

摘要： “通过微分公式调查无限级数求和的简明方法”（1780年）的翻译。 欧拉想要以另一种方式表示一些给定的函数级数 S(x)=X(x)+X(x+1)+X(x+2)+等。 他将S写成X的导数的级数，系数未知。 他从这些系数中构造出一个生成函数V(z)，这与涉及伯努利数的生成函数相同。 显示英文摘要

摘要： 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.