Chapter 4: Series and infinite products of real numbers

This chapter discusses the convergence of number series, including power series and double series. Along with widespread convergence criteria, such as d'Alembert, Cauchy, Raabe, Leibniz, Dirichlet, and Abel, we also consider the universal Gauss criterion, the deep Riemann theorem on rearrangements of conditionally convergent series, and the Mertens theorem on double series. In addition, the principles of infinite products make it possible to introduce (by an equivalent and rather simple method) Euler's Gamma function and treat many of its properties.