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The series or functional series is one of the approaches to studying the theory of the functional approximations and calculus and is one of the important research objects of analytical mathematics. There are many cases in which quantities used in various practical fields of natural science and technology, including mechanical, thermal, and design calculations, are represented in series form. Therefore, the theory of series is an important place in the research and mathematical theory development of modern science and technology. The most important issue in the theory of series is to study the convergence of series. It is just the convergence evaluation of the series that is not important to find the sum of the series. Hence, we will discuss the convergence theory and the problem of series in this book. As can be seen in the examples presented in Chapter 2, it is not possible to properly evaluate the accuracy of scientific and technical calculations or the accuracy of the evolvingcontent without knowing the convergence of the series of handoffs, convergence of the series of functions, and uniform convergence.