An introduction to the topics presented at the conference “Approximation and extrapolation of convergent and divergent sequences and series” CIRM Luminy: September 28, 2009–October 2, 2009

The conference “Approximation and extrapolation of convergent and divergent sequences and series” discusses some very old problems of mathematical analysis and modern approaches for their solution based on so-called nonlinear sequence transformations. In spite of all the advances in computer hard and software, slowly convergent or divergent sequences and series are still annoying obstacles not only in mathematics, but in particular also in other mathematically oriented disciplines. This articles tries to give a highly condensed survey of the topics treated at this conference.