Although 70 years old, J. Barkley Rosser has written a nice article on the Transformations to Speed the Convergence of (Convergent) Series. https://bit.ly/2m70WHz (Rosser was a past president of SIAM as well as a student of Alonzo Church.)
Thank you very much for pointing this out. I have long been aware of the art of convergence acceleration, and over the years have seen various scattered examples of its application; but this is a particularly illuminating glimpse into the practice of a master.