True-False Quiz Question 16: Monotonic Sequence Theorem

In this video I show that a sequence is convergent, by the Monotonic Sequence Theorem, if it is positive and decreasing for all values of n. This would mean that the sequence is bounded because the largest value would be the initial term and the smallest value is a number greater than 0. Thus we can apply the Monotonic Sequence Theorem and the sequence is convergent. We can see this visually since the terms of the sequence will approach a limit L greater than 0. Thus, the answer to our question is True.

Time stamps:

• Question 16: 0:00
• Solution: True: 0:23
• Monotonic Sequence Theorem: 0:43

Full video below:

• Infinite Sequences and Series: Review and True-False Quiz:
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• Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L

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