By：Tao Steven Zheng (鄭濤)

Nicole Oresme (c. 1320 – 1382) was an influential French philosopher, theologian, and mathematician during the late Middle Ages. In mathematics, Oresme made important contributions to the study of proportion and infinite series. Among his most famous mathematical works are ''Tractatus de configurationibus qualitatum et motuum ''and ''Algorismus proportionum''.

【Problem】

Determine the following infinite series:

【Solution】

Nicole Oresme gave a geometric argument for solving this infinite series. The following demonstration is an arithmetic interpretation of Oresme’s method. Nicole Oresme explained this argument geometrically, as shown in the figure below, but we will actually calculate the series using modern mathematical notation.