Monotonic Sequences and Examples

In this video I go over the definition of increasing and decreasing sequences, which are thus denoted as Monotonic. An increasing sequence has each consecutive term bigger than the previous, while a decreasing sequence has each consecutive term bigger than the previous. I illustrate this in two examples, which we can determine by manually plugging in n and n + 1 inside the sequence and identifying which term is bigger. In the second example, I also show that we can use the derivative (via the quotient rule) to find if a sequence is increasing or decreasing. Since the derivative of the corresponding function is negative, the sequence must be decreasing!

#math #sequences #calculus #education #monotonicity

Timestamps:

- Definition 4: Increasing and decreasing sequences are called Monotonic: 0:00
- Example 11: 3 / (n+5): 1:50
- Example 12: n / (n^2+1): 3:28
- Solution 1: Directly evaluating the terms: 3:40
- Solution 2: Using derivatives via quotient rule: 7:52
- Derivative is negative so the sequence is decreasing: 11:06

Notes and playlists:

- Summary: https://inleo.io/threads/view/mes/re-leothreads-2q4zl9g8z
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUgfK34Voi6BvrNqt4X4BV
- Notes: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more
- Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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