Review Question 8: Power Series, Radius and Interval of Convergence
In this video I recap on power series and the conditions that it converges, that is, its radius and interval of convergence. A power series has terms of the form: constant * (x - a)^n. There are only three possibilities for its convergence: Either it converges only for x = a, or converges for all x, or it converges for |x - a| is less than the radius of convergence R. In the first case, the radius of convergence is considered as R = 0, and the second case it is R = infinity. The interval of convergence has 4 possibilities, since at |x - a| = R, the series can converge or diverge. Thus the interval of convergence is either (a - R, a + R), (a - R, a + R], [a - R, a + R), or [a - R, a + R]. I also graphically show this in the video.
The timestamps of key parts of the video are listed below:
- Question 8: 0:00
- (a) General form of a power series: 0:20
- (b) Radius of convergence of a power series: 1:11
- Summary for the radius of convergence: 6:28
- (c) Interval of convergence of a power series: 7:40
This video was taken from my earlier video listed 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:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
------------------------------------------------------
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
Like, Subscribe, Favorite, and Comment Below!
Follow us on:
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
MORE Links: https://linktr.ee/matheasy
Email me: contact@mes.fm
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
-
3:37
Math Easy Solutions
5 months ago $0.01 earnedTrue-False Quiz Question 6: Divergence by Radius of Convergence Theorem
1211 -
9:32
Math Easy Solutions
6 months ago $0.06 earnedReview Question 9: Derivative and Integral of Power Series
1931 -
4:09
mh-math
4 months agounit circle and trigonometric functions.
17 -
2:57
DrOfEng
1 month agoConfirming Continuity over an Interval, Examples - AP Calculus AB/BC
3 -
3:12
DrOfEng
2 months agoDetermine Limits using the Squeeze Theorem - AP Calculus AB/BC
3 -
1:10
DrOfEng
1 month agoConfirming Continuity over an Interval - AP Calculus AB/BC
4 -
1:03
Minute Math
1 month ago $0.01 earnedVertices and Edges Explained | Graph Theory Basics
22 -
2:17
DrOfEng
3 months agoGeometric Series, Iteration and Recursion - Discrete Mathematics
8 -
1:30
Ascencore
5 months agoTLRY Chart Analysis With The Advance Decline IndicatorAdvance DeclineBreadth indicator
17 -
2:35
DepEd Trends
27 days agoMATH 5 Summative test
2822