True-False Quiz Question 6: Divergence by Radius of Convergence Theorem

In this video I show that if a power series with powers 6^n is divergent by the Radius of Convergence Theorem then the series with powers 10^n is also divergent. A power series has 3 conditions, it's either convergent at x = a = 0 in our case, or converges for all x, or converges whenever |x - a| is less than R, termed the radius of convergence. In our case, x = 6 and a = 0, but the series diverges, so R is less than 6. This means that R is less than 10 as well, so our given series is also divergent.

Time stamps:

- Question 6: 0:00
- Solution: True: 0:25
- Radius of convergence R is less than 6: 1:51
- R is less than 10 so our series diverges too: 2:44

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

Related Videos:

Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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