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Sep 29, 2021 · Learn the definitions and differences of divergence and convergence in the context of trends, prices, and indicators in economics and finance. Divergence means two things move apart, while convergence means they move together.
Nov 16, 2022 · In this section we will discuss in greater detail the convergence and divergence of infinite series. We will illustrate how partial sums are used to determine if an infinite series converges or diverges.
Converging means something is approaching something. Diverging means it is going away. So if a group of people are converging on a party they are coming (not necessarily from the same place) and all going to the party.
Notice that a sequence converges if the limit as n approaches infinity of An equals a constant number, like 0, 1, pi, or -33. However, if that limit goes to +-infinity, then the sequence is divergent.
In practice, explicitly calculating this limit can be difficult or impossible. Luckily, several tests exist that allow us to determine convergence or divergence for many types of series. In this section, we discuss two of these tests: the divergence test and the integral test.
How can we show convergence vs. divergence? When can we use the usual rules for finite sums in the infinite case? 1.1 Convergence vs. divergence. We view infinite sums as limits of partial sums. Since partial sums are sequences, let us first review convergence of sequences. Definition 1.
Determine the convergence or divergence of a given sequence. We show how to find limits of sequences that converge, often by using the properties of limits for functions discussed earlier. We close this section with the Monotone Convergence Theorem, a tool we can use to prove that certain types of sequences converge.
