## Examples 3.3.2(a):

Take the sequence
.
Extract every other member, starting with the first. Then do
the same, starting with the second.

The sequence in question is
If we extract every second number, starting with the first, we get:= {-1, 1, -1, 1, -1, 1, ...}

This subsequence now converges to -1.{-1, -1, -1, -1, ...}

If we extract every second number, starting with the second, we get:

This subsequence now converges to 1.{1, 1, 1, 1, 1, ...}