Almost Convergent Sequence/Examples

Examples of Almost Convergent Sequence

Example: $\sequence {0, 1, 0, 1, \ldots}$ almost converges to $1/2$

Let $\sequence {x_n}_{n \in \N}$ be the sequence defined by:

$x_n = \begin{cases} 0 & : n \equiv 0 \pmod 2 \\ 1 & : n \equiv 1 \pmod 2 \end{cases}$

where $\bmod$ denotes the congruence modulo.

Then $\sequence {x_n}_{n \in \N}$ almost converges to $1/2$.