The sum of an infinite series whose final term vanishes perhaps is infinite, perhaps finite.- Jacob Bernoulli
XLII. PROPOSITIO DE SCALA HABENTE GRADVS CENTVM.
Est scala una habens gradus C. In primo gradu sedebat columba una: in secundo duae; in tertio tres; in quarto IIII; in quinto V. Sic in omni gradu usque ad centesimum. Dicat, qui potest, quot columbae in totum fuerunt?
42. PUZZLE OF THE HUNDRED STEPS
There is a ladder which has 100 steps. One pigeon sat on the first step, two pigeons on the second, three pigeons on the third, four on the fourth, five on the fifth, and so on up to the hundredth step. How many pigeons were there in total on the ladder?