Convergence & divergence of telescoping series

Lessons

• Introduction
  Telescoping Series Overview:

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• 1.
  Convergence of Telescoping Series
  Show that the following series are convergent and find its sum:
  
  a)

  $\sum_{n=1}^{\infty}\frac{4}{n^2+7n+12}$
  
  
  b)

  $\sum_{n=1}^{\infty}\frac{1}{n^2+4n+3}$
  
  
  c)

  $\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$
  
  

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• 2.
  Divergence of Telescoping Series with different pattern
  Show that the series $\sum_{n=1}^{\infty}(-1)^n$ is a diverging telescoping series.
  

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