In the master's thesis we will discuss conditionally convergent infinite number series. We will look at how and when the order of the summation terms of such a number series affects the sum itself. For conditionally convergent series with real terms, Riemann series theorem tells us that with appropriate rearrangement the sum of the series can be an arbitrary number. We will examine some specific rearrangements and corresponding sums of alternating harmonic series, the Schlömilch theorem and the Pringsheim theorem for alternating series. In a complex case, we will study the more challenging Lévy–Steinitz theorem, which says that the set of all possible sums is either a line in a complex plane or the entire complex plane.
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