About a historical note on a famous series

Question

Currently, I'm doing research on the history of the Basel problem and I happen to notice a small gap. Not on the history of the aforementioned problem per se, since its history is very well documented. In fact, I mean that I wasn't able to determine who was the first person to show the convergence of the series of reciprocals of squares, before its exact value was determined by Leonhard Euler. Although, I did, quite coincidentally I may add, come across a random comment on a post about a proof of the convergence of the series in discussion, saying that Bernoulli (unfortunately, not which member of the Bernoulli family) showed the convergence by bounding the series from above by the number 2. Sadly, it wasn't mentioned whether a Bernoulli brother was the first person to achieve such a result. In case that the previous holds to be true, I kindly ask for anyone to verify such claim. Otherwise, I ask of you to tell/find me that person and with robust evidence such as sources and web links. You are thanked and muchly appreciated a priori for this endeavour. Have a good day.

Answer 1

According to W. Gautschi 2008:

Stirling, already in 1730, actually calculated the series to nine decimal places, but Euler did not yet know this.

DOI. 10.1137/070702710