Comparison & limit comparison test

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Intros
Lessons
  1. Overview:

  2. Comparison test
  3. Limit Comparison test
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Examples
Lessons
  1. Convergence & Divergence of Comparison Tests
    Use the Comparison Test to determine if the series converge or diverge.
    1. n=112n+5 \sum_{n=1}^{\infty}\frac{1}{2^n+5}
    2. n=1n4+5n5sin4(2n) \sum_{n=1}^{\infty}\frac{n^4+5}{n^5-sin^4(2n)}
    3. n=1n4cos4(7n)1n6 \sum_{n=1}^{\infty}\frac{n^4cos^4(7n)-1}{n^6}
  2. Convergence & Divergence of Limit Comparison Tests
    Use the Limit Comparison Test to determine if the series converge or diverge.
    1. n=3n2+n3n8+n4 \sum_{n=3}^{\infty}\frac{n^2+n^3}{\sqrt{n^8+n^4}}
    2. n=11n27n12 \sum_{n=1}^{\infty}\frac{1}{n^2-7n-12}
  3. Understanding of Both Tests
    Use both the comparison and limit comparison test for the series k=1k31k32k2+5\sum_{k=1}^{\infty}\frac{\sqrt{k^3-1}}{k^3-2k^2+5} . What do both tests say?