True-False Quiz Question 11: Convergent Sequence r^n when |r| is less than 1
In this video I show that the sequence r^n is convergent and is equal to 0 when r is between 1 and -1. This is because a number whose absolute value is less than 1 becomes smaller and smaller each time it is multiplied. The negative sign only has it changing from positive to negative but the absolute value still becomes smaller. Thus the answer to the question is True. Note also when r = 1, the sequence is also convergent but it equals 1 since 1^n is always equal to 1.
Time stamps:
- Question 11: 0:00
- Solution: 0:14
- Visual illustration: 1:17
- Visualization of powers of negative r: 2:34
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
-
3:21
Math Easy Solutions
9 days ago $0.03 earnedTribute to Dominique Radwanski (1979 - 2016). Creator of Somewhere Out There (2007) Documentary
1322 -
14:45
GeekyNerdyTechy
22 hours agoZHIYUN MOLUS X60 RGB LED Combo Review & Tutorial
32.4K -
9:49:05
SquallRush
10 hours agoBrawlhalla then Monster Hunter @sandking0077
20.7K5 -
2:25:39
JTT Show
13 hours agoI Accidentally Got In Bed With My Father-In-Law
22.8K9 -
3:08:57
Spittin' Chiclets
14 hours agoBoston vs. Toronto Game 7 Livestream
39.5K7 -
6:50:45
Akademiks
14 hours agoKendrick Lamar spins the Block on Drake AGAIN!! Disses him again and even BIG AK gets a bar!
141K72 -
1:24:41
LFA TV
1 day agoLAST CALL WITH MIKE CRISPI | FT. JEREMY HERRELL & SHAWN FARASH | 5.4.24 8PM
65.5K65 -
1:49:51
Darkhorse Podcast
1 day agoNever Alone: The 223rd Evolutionary Lens with Bret Weinstein and Heather Heying
78.8K62 -
2:22:22
Jewels Jones Live
1 day agoWEAPONIZATION | A Political Rendezvous - Ep. 75 - 5/4/2024
81.2K58 -
1:35:13
Roseanne Barr
1 day ago $12.26 earnedGuns And Chardonnay | The Roseanne Barr Podcast #46
166K334