Limit of a Number Sequence

Limit of a Number Sequence

Value to which the terms in a number sequence extend.

When a sequence has a limit, we say that it converges; if it does not, we say that it diverges.


  • The following sum has a limit of 0, because its terms can approach 0 as close as we like, while remaining positive; this sequence converges toward 0:
    1, \(\dfrac{1}{2}\), \(\dfrac{1}{4}\), \(\dfrac{1}{8}\), \(\dfrac{1}{16}\), \(\dfrac{1}{32}\), …
  • The following sequence diverges, because its limit is infinite: 1, 3, 5, 7, 9, 11, 13, …

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