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Lecture 8-4

# Lecture 8-4 - 1 ∞ X n =1 1 2 √ n 3 √ n 2 ∞ X n =1 n...

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8.4 - Comparison Tests The Direct Comparison Test (DCT) Suppose 0 a n b n for n N for some integer N . Then 1. 2. Examples Determine whether the following series converge or diverge. 1. X n =1 | sin n | n 2 2. X n =10 1 n - 3 1

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3. X n =1 5 2 + 3 n 4. X n =1 1 2 n + 3 n The Limit Comparison Test (LCT) Suppose a n > 0 and b n > 0 for all n N for some integer N . 1. 2. If lim n →∞ a n b n = 0 and b n converges, then a n converges. 3. If lim n →∞ a n b n = and b n diverges, then a n diverges. 2
Examples

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Unformatted text preview: 1. ∞ X n =1 1 2 √ n + 3 √ n 2. ∞ X n =1 n + 2 n 2-5 n + 1 3. ∞ X n =1 ( n + 1)(2 n-1) ( n 2 + n-1) 3 4. ∞ X n =1 1 2 n-1 5. ∞ X n =1 8 n + 3 n ( n + 5)( n + 7) 4 Do. Determine if the following series converge or diverge. 1. ∞ X n =1 2 n √ 3 n + 1 2. ∞ X n =1 3 n 2 n 5...
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