Note Monotonic Sequences
**Let
be a non-decreasing sequence.
- If
is bounded above, then converges to - If
is not bounded above, then diverges to . In particular,
converges if and only if it is bounded above.**
The LUB GLB (sup, inf) properties have been described here.
Let
Since
If
Since
A similar statement can be made about non-increasing sequences by replacing the infimum with the supremum and
