Limit of a Number Sequence

Examples

• 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, …