Premium Only Content

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
-
1:58:35
Math Easy Solutions
8 days agoMES Math Q/A 28: What is a Plasmoid?
1801 -
44:45
The White House
1 hour agoPresident Trump Signs an Executive Order, July 31, 2025
9405 -
LIVE
Sarah Westall
1 hour ago“This Conversation Would Land Me in Prison in Ireland” - Its the Global Plan w/ Captain Kieran Kelly
235 watching -
1:15:42
vivafrei
2 hours agoPelosi Doth Protest Too Much! "Trans" Athlete Plot to Harm Female? Crooked hillary Cooked & MORE
73.1K20 -
1:42:17
The Quartering
4 hours agoHillary Clinton FINALLY BUSTED, Nancy Pelosi MELTDOWN, Kamala Harris Admits Defeat & More
101K63 -
3:10:42
Barry Cunningham
8 hours agoMUST SEE: KAROLINE LEAVITT HOSTS WHITE HOUSE PRESS CONFERENCE ( AND MORE NEWS)
43.9K19 -
53:03
Sean Unpaved
5 hours agoSchlereth Unplugged: 3x Champ Talks TV, Football, & 2025 Season Expectations
29.3K -
1:03:28
Russell Brand
5 hours agoCan You Really Take an Unbiased Look at Hitler? - SF624
135K103 -
12:39
Michael Button
7 hours ago $1.47 earnedAn Entire Civilization Might Be Buried Under the Sahara
23.9K9 -
4:38
Michael Heaver
12 hours agoShifting UK Triggers Rapid REVOLUTION
20.9K2