ヤコブ・ベルヌーイ
Jacob Bernoulli (1654–1705) dealt with a similar series in 1696 in the third part of his "Positiones arithmeticae de seriebus infinitis". Applying Nicholas Mercator's method for polynomial long division to the ratio , he noticed that one always had a remainder. If then this remainder decreases and "finally is less than any given quantity", and one has