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sec11_4 - c is a real number with c> Then ± a n...

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11.4 The Comparison Test 1. The Comparison Test Theorem 1.1 (Comparison Theorem) . If { a n } , { b n } , and { c n } are sequences with 0 a n b n c n then (1) If n =1 a n then n =1 b n also . (2) If n =1 c n then n =1 b n also . Example 1.1. (problem 12) Determine whether the Series Converges or Diverges. Explain. n =1 1 + sin n 10 n Example 1.2. Determine whether the Series Converges or Diverges. Explain. n =1 1 2 n - 5 1
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Section 11.4 Comparison Tests 2 2. Limit Comparison Test Theorem 2.1 (Limit Comparison Test) . Suppose a n 0 , b n 0 , and lim n →∞ a
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Unformatted text preview: c is a real number with c > . Then ± a n converges if and only if ± b n converges. Example 2.1. Determine whether the Series Converges or Diverges. Explain. ∞ ± n =1 1 2 n-1 Example 2.2. (problem 18) Determine whether the Series Converges or Diverges. Explain. ∞ ± n =1 1 2 n + 3 Example 2.3. (problem 30) Determine whether the Series Converges or Diverges. Explain. ∞ ± n =1 n ! n n...
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