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Convergence & divergence of telescoping series

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Intros
Lessons
  1. Telescoping Series Overview:
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Examples
Lessons
  1. Convergence of Telescoping Series
    Show that the following series are convergent and find its sum:
    1. ∑n=1∞4n2+7n+12\sum_{n=1}^{\infty}\frac{4}{n^2+7n+12}
    2. ∑n=1∞1n2+4n+3\sum_{n=1}^{\infty}\frac{1}{n^2+4n+3}
    3. ∑n=1∞14n2−1\sum_{n=1}^{\infty}\frac{1}{4n^2-1}
  2. Divergence of Telescoping Series with different pattern
    Show that the series ∑n=1∞(−1)n \sum_{n=1}^{\infty}(-1)^n is a diverging telescoping series.