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
-
3:04:50
Math Easy Solutions
7 days ago $0.10 earnedMES Livestream 26: Project Blue Beam Deep Dive
2043 -
11:20
Hannah Barron
16 hours agoLife with Hannah! More Than Social Media!
3.27K14 -
8:24:29
Act Files
9 days agoThe IMPACT | Groundbreaking Documentary
9.66K15 -
7:50
Brad Polumbo
15 hours agoCNN hits new level of (woke) insanity!
1.79K12 -
2:44:29
Steven Crowder
15 hours agoBiden’s Fail the Nation Address
528K843 -
57:45
Man in America
20 hours ago🔴 LIVE: Something STRANGE is Happening w/ Biden | Trump Shooter MK-Ultra?
49.7K76 -
54:17
LFA TV
1 day agoManufacturing Enthusiasm for Kamala | Trumpet Daily 7.24.24 9pm EST
76.8K8 -
2:10:31
Fresh and Fit
12 hours agoPop The Balloon Reaction Part 2
123K31 -
1:31:16
Kim Iversen
15 hours agoAmazon REMOVES Books Critical Of Kamala Harris | Netanyahu Claims Israel Killed “Practically No” Civilians
137K186 -
1:49:40
Glenn Greenwald
15 hours agoNetanyahu's Speech To Congress; Project 2025: Untangling Fact From Fiction with Heritage Foundation President Kevin Roberts; PLUS: Max Blumenthal on Israel | SYSTEM UPDATE #303
175K300