section_path: Properties of series/Absolute convergence
section_name: Absolute convergence
paragraph_text: Absolute convergence
  
  A series
  
  ∑ n = 0 ∞ a n {\displaystyle \sum _{n=0}^{\infty }a_{n}}
  
  converges absolutely if the series of absolute values
  
  ∑ n = 0 ∞ | a n | {\displaystyle \sum _{n=0}^{\infty }\left|a_{n}\right|}
  
  converges. This is sufficient to guarantee not only that the original series converges to a limit, but also that any reordering of it converges to the same limit.