Premium Only Content

True-False Quiz Question 4: Radius of Convergence Theorem and Comparison Test
In this video I show that if we are given that a power series of the form 6^n is convergent, then a power series of the form (-2)^n is also convergent by the radius of convergence theorem and also the comparison test. The radius of convergence theorem states that a power series has only 3 possibilities for convergence: the series converges only for x = a = 0 in our case, the series converges for all x, or it converges for |x - a| is less than R. In our case the 6^n means that it is convergent for R is less than 6, which is greater than 2, thus our given series is also convergent. Likewise, we can compare the positive form of our power series with the convergent power series to show that it too is convergent, since all the terms would be less than the convergent series. And if a series is absolutely convergent than it is also convergent, thus proving our case.
Timestamps:
- Question 4: 0:00
- Solution 1: True: Radius of Convergence Theorem: 0:18
- Solution 2: Comparison Test: 7:02
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 .
------------------------------------------------------
Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
MES Links: https://mes.fm/links
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
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
-
56:19
Math Easy Solutions
9 days ago $0.12 earnedAnimal Form and Function: Immune System
1624 -
LIVE
Badlands Media
1 hour agoDevolution Power Hour Ep. 382
23,663 watching -
2:06:30
Inverted World Live
5 hours agoDon't Approach the Zombie Rabbits | Ep. 95
22.4K7 -
LIVE
Drew Hernandez
1 hour agoISRAEL PLANNING POSSIBLE DRAFT IN USA & TRUMP'S VIEW ON ETERNAL LIFE ANALYZED
1,112 watching -
3:08:07
TimcastIRL
4 hours agoTexas Republicans Win, House Passes Redistricting Map, GOP Looks To Gain 5 Seats | Timcast IRL
144K53 -
1:30:34
FreshandFit
4 hours agoHow To Stay Focused While Pursuing Women...The Good, The Bad, And The Ugly
30.9K20 -
1:47:05
Drew Hernandez
8 hours agoISRAEL PLANNING POSSIBLE DRAFT IN USA & TRUMP'S VIEW ON ETERNAL LIFE ANALYZED
20.2K55 -
29:55
Afshin Rattansi's Going Underground
3 days agoProf. Omer Bartov: The REAL REASON the US, UK, and EU Have Not Recognised Israel’s Genocide in Gaza
14.6K24 -
LIVE
SpartakusLIVE
6 hours agoWednesday WZ with the Challenge MASTER || Duos w/ GloryJean
403 watching -
2:36:12
Barry Cunningham
5 hours agoREACTING TO STEPHEN MILLER | KASH PATEL | TULSI GABBARD INTERVIEWS AND MORE NEWS!
62.3K60