3.3. Subsequences
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
= {-1, 1, -1, 1, -1, 1, ...}If we extract every second number, starting with the first, we get:
{-1, -1, -1, -1, ...}This subsequence now converges to -1.
If we extract every second number, starting with the second, we get:
{1, 1, 1, 1, 1, ...}This subsequence now converges to 1.