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Testing Series Convergence Using the Limit Definition

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Explanations 2

Previously, we began to talk about infinite series, and how they behave. Here, we'll continue that discussion with an emphasis on the limit definition of an infinite series. Let…
By Steven Kwon, Avi Romanoff, Moor Xu, Victor Wang
Using the Limit Definition to Test for Series Convergence How do you determine whether an infinite series converges or diverges? In the simplest cases, you can stick to the basi…
By Victor Wang

Problems 1

Let {an}\{a_n\}{an} be a sequence which converges to a value aaa, and define a sequence {bn}\{b_n\}{bn} via b0=a0b_0 = a_0b0=a0 and bn=an−an−1b_n = a_n - a_{n-1}bn=an−an−1…