page_title: Limit of a sequence
hierarchical_section_title: Limit of a sequence
context_page_description: In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to", and is often denoted using the symbol. If such a limit exists, the sequence is called convergent. A sequence that does not converge is said to be divergent. The limit of a sequence is said to be the fundamental notion on which the whole of mathematical analysis ultimately rests.
  Limits can be defined in any metric or topological space, but are usually first encountered in the real numbers.
context_section_description: In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to", and is often denoted using the  symbol (e.g., ). If such a limit exists, the sequence is called convergent. A sequence that does not converge is said to be divergent. The limit of a sequence is said to be the fundamental notion on which the whole of mathematical analysis ultimately rests.
  Limits can be defined in any metric or topological space, but are usually first encountered in the real numbers.
caption: The sequence given by the perimeters of regular n-sided polygons that circumscribe the unit circle has a limit equal to the perimeter of the circle, i.e. 
    
      
        
          2
          π
          r
        
      
      {\displaystyle 2\pi r}
    
  . The corresponding sequence for inscribed polygons has the same limit.