filmov
tv
Monotonic Sequences - Increasing Decreasing Sequences
Показать описание
In this video we will learn about "Monotonic Sequences - Increasing and Decreasing Sequences"
In mathematics, monotonic sequences are sequences whose terms consistently increase or decrease. These sequences exhibit a predictable pattern of behaviour, either growing larger or smaller as the sequence progresses.
1. Monotonic Sequence
A sequence {an}{an} is called monotonic if it is either entirely increasing or decreasing (or both).
2. Increasing Sequences
A sequence is increasing if each term is greater than or equal to the previous term.
3. Decreasing Sequences
A sequence is decreasing if each term is less than or equal to the previous term.
4. Properties of Monotonic Sequences
Boundedness:
A monotonic sequence that is bounded (above for increasing, below for decreasing) will always converge to a limit.
Unboundedness:
If a monotonic sequence is not bounded, it diverges to infinity (∞∞) or negative infinity (−∞−∞).
Monotonic Convergence Theorem:
Every bounded monotonic sequence converges.
In mathematics, monotonic sequences are sequences whose terms consistently increase or decrease. These sequences exhibit a predictable pattern of behaviour, either growing larger or smaller as the sequence progresses.
1. Monotonic Sequence
A sequence {an}{an} is called monotonic if it is either entirely increasing or decreasing (or both).
2. Increasing Sequences
A sequence is increasing if each term is greater than or equal to the previous term.
3. Decreasing Sequences
A sequence is decreasing if each term is less than or equal to the previous term.
4. Properties of Monotonic Sequences
Boundedness:
A monotonic sequence that is bounded (above for increasing, below for decreasing) will always converge to a limit.
Unboundedness:
If a monotonic sequence is not bounded, it diverges to infinity (∞∞) or negative infinity (−∞−∞).
Monotonic Convergence Theorem:
Every bounded monotonic sequence converges.
0:05:57
Monotonic Sequences - Increasing Decreasing Sequences
0:31:23
Monotonic Sequences and Bounded Sequences - Calculus 2
0:08:40
Sequences - Increasing, decreasing, bounded and monotonic sequences
0:12:41
What are Monotone Sequences? | Real Analysis
0:02:50
Determine if sequence is increasing or decreasing, not monotonic, bounded {(2n-3)/(3n +4)}
0:15:29
How to prove monotone sequences
0:11:38
Increasing, decreasing and not monotonic sequences (KristaKingMath)
0:36:03
Monotonic Sequence, Eventually Monotonic Sequence with examples | Sequence of real numbers : 02
0:08:11
Exercises 10A. Examples of monotone increasing and decreasing sequences.
0:05:42
Video 11.1.10: Increasing, Decreasing, and Monotonic Sequences
0:10:54
Monotone Sequence | Monotonically increasing | Monotonically decreasing | Definition | Examples
0:01:57
Determine if sequence is increasing, decreasing, or not monotonic, bounded {1/(2n+3)}
0:13:26
Real Analysis | Monotonic Sequence - Bounded Sequence | Definition & Examples
0:17:31
5 Bounded and monotonic sequences
0:08:02
How to Determine if a Sequence is Monotonic and Bounded: Example with n/(n^2 + 1)
0:41:57
Monotonic and Bounded Sequences | Calculus 2 | Math with Professor V
0:00:15
Monotonic Sequence #realanalysis
0:10:22
Monotonic Sequences
0:32:53
Unit 3 Video 5 Monotonic and Bounded Sequences
0:11:49
11.1.5 Increasing, Decreasing, Monotonic, and Bounded Sequences
0:02:58
11.1.72 Determine whether the sequence is increasing, decreasing, or not monotonic. an = (-2)^(n+1)
0:09:04
Ch 9-1 Monotonic and Bounded Sequences (Ex 8-9)
0:07:48
11.1.78 Determine whether the sequence is increasing, decreasing, or not monotonic. an = n + 1/n
0:04:54
Monotonic Sequence Theorem - Full Example Explained
Комментарии