Convergence and divergence of normal infinite series

Lessons

• Introduction
  Overview of Converging and Diverging Series

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• 1.
  Converging and Diverging Series with the formula of partial sums
  
  You are given the general formula of partial sums for the following series. Determine whether the series converges or diverges.
  
  a)

  $\sum_{n=1}^{N}a_n=\frac{N^2+2N+3}{N+6}$
  
  
  b)

  $\sum_{n=1}^{N}a_n=\frac{N^2+6N+2}{N^2+4}$
  
  
  c)

  $\sum_{n=1}^{N}a_n=\frac{N+5}{N^2+1}$
  
  

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• 2.
  Converging and Diverging Series without the formula of partial sums
  
  Determine whether the following series converges or diverges.
  
  a)

  $\sum_{n=1}^{\infty}n$
  
  
  b)

  $\sum_{n=1}^{\infty}n^3$
  
  
  c)

  2+4+6+8+ ...
  
  

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