Lec 25 - Sequences & Series
Increasing, decreasing, monotonic, bounded sequence.
Aside: Completeness Axiom
If a set of real numbers has an upper bound then there is a least upper bound.
Theorem: Monotonic Sequence Theorem
Every bounded, monotonic sequence is convergent.
By the axiom above, if it is bounded there is a least upper bound.
Play with the sequence
Taking the limit,
An infinite series is an infinite sum of a sequence,
The geometric series is the sum of the geometric sequence.
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