Limit of a sequence

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., ).[1] If such a limit exists, the sequence is called convergent.[2] A sequence that does not converge is said to be divergent.[3] The limit of a sequence is said to be the fundamental notion on which the whole of mathematical analysis ultimately rests.[1]

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. The corresponding sequence for inscribed polygons has the same limit.
nn sin(1/n)
10.841471
20.958851
...
100.998334
...
1000.999983

As the positive integer becomes larger and larger, the value becomes arbitrarily close to We say that "the limit of the sequence equals "

Limits can be defined in any metric or topological space, but are usually first encountered in the real numbers.


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