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Lecture 8-2 - 8.2 Innite Series Defn Innite Series An...

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8.2 - Infinite Series Defn. Infinite Series An infinite series is an infinite sum of a sequence of real numbers. a n = s n = Examples 1. X n =1 n 2. X n =1 1 n 3 1
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Defn. Series Convergence or Divergence An infinite series converges and has sum “ s ” if the sequence of partial sums { s n } converges to s . If { s n } diverges, then the series diverges . To determine convergence or divergence of a series, we look at specific kinds of series and we also will learn several tests that can be used. Let’s start with two kinds of series: Geometric Series and Telescoping Series. Geometric Series Defn. Geometric Series A geometric series has the form where a and r are real numbers, a 6 = 0. 2
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Examples of Geometric Series 1. 2 + 4 + 8 + 16 + · · · + 2 n + · · · 2. X n =1 ( - 1) n 5 4 n Let’s determine the partial sums of geometric series and how to tell if they converge or diverge. To do so, we’ll look at 3 cases for the value of r .
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