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Unformatted text preview: =1 tan1 ( n ) 1 + n 2 2. ∞ X n =22 n + 1 3 Note: The integral test requires that n starts at a POSITIVE integer. If n starts at 0 for example, use the integral test as if n starts at 1. Since you are leaving oﬀ a ﬁnite number of terms (in this case, just one. .. namely the term for when n = 0) the conclusion of the integral test for the series starting at 1 will give the same conclusion for the series starting at n = 0. Defn. pseries A pseries is a series of the form where p is a real number. The pseries Test Suppose ∞ X n =1 a n is a pseries. Then, 1. 2. Note: ∞ X n =1 1 n is called the harmonic series , i.e. the pseries where p = 1. 4 Examples Determine whether the following series converge or diverge. Justify your answer. 1. ∞ X n =18 n 5 / 2 2. ∞ X n =1 1 n 2 + 5 √ n Do. Determine if ∞ X n =1 2 n √ n converges or diverges. Justify your answer. 5...
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 Spring '03
 MECothren
 Multivariable Calculus, Order theory

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