By 1689 he had published important work on infinite series and published his law of large numbers in probability theory. Jacob Bernoulli published five treatises on infinite series between 1682 and 1704 The first two of these contained many results, such as the fundamental result that formula_1 diverges, which Bernoulli believed were new but they had actually been proved by Pietro Mengoli 40 years earlier. Bernoulli could not find a closed form for formula_2, but he did show that it converged to a finite limit less than 2. Euler was the first to find the sum of this series in 1737. Bernoulli also studied the exponential series which came out of examining compound interest.