Name: True-False Quiz Question 8: Applying the Ratio Test to Show Convergence
Uploaded: 2024-01-11T03:54:50+00:00
Duration: 3 min 15 s
Description: In this video I show that the series with terms 1/n! converges by the Ratio Test. The Ratio Test states that the limit as n approaches infinity of the absolute value of the ratio of terms a_n+1 / a_n

1 year ago

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Health & Science Education math science stem calculus ratio test convergence limits convergent divergent

In this video I show that the series with terms 1/n! converges by the Ratio Test. The Ratio Test states that the limit as n approaches infinity of the absolute value of the ratio of terms a_n+1 / a_n converges if it equals to a number less than 1, diverges if greater than 1, and inconclusive if equal to 1. In our case, I show that the Ratio Test is equal to 0, which is less than 1. Hence our given series converges and the answer to the question is True.

Time stamps:

- Question 8: 0:00
- Solution: True: 0:15
- Ratio Test = 0 = Converges: 2:38

Full video below:

- Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L