True-False Quiz Question 22: Multiplication of Terms of Series May NOT Equal Multiplication of Sums
In this video I show that if we have two infinite series whose sums are A and B, then a third series comprising of both terms multiplied by each other may not sum to AB. I show this by considering two convergent Geometric Series. The first series has terms (0.1)^n and the sum is 1/9. The second series has terms (0.2)^n and the sum is 1/4. Thus AB = 1/36. If we multiplied the terms of each series to form a new series we get a series with terms (0.02)^n. The sum of this new series, using the formula for the sum of a convergent Geometric Series, is 1/49. But this is not the same as the value AB = 1/36. Thus the answer to our question is False.
Time stamps:
- Question 22: 0:00
- Solution: False: 0:38
- Testing question with Geometric Series: 0:53
- First Series: Sum = A = 1/9: 1:25
- Second Series: Sum = B = 1/4: 2:56
- Sum of multiplication series = 1/49: 4:03
- Multiplying sums = AB = 1/36: 6:48
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
-
2:43:40
Math Easy Solutions
4 days agoMES Livestream 17: New Year Emergency Broadcast
1372 -
8:03
Kicking Mustang
1 day agoUsing my Ghillie Suit to Sneak Attack Clueless Enemies..
24.8K3 -
2:47
Maicy Renee
21 hours agoSounds Like a Terrible Night!
21K13 -
18:23
Crypto Crew University
1 day agoWARNING: BITCOIN ABOUT TO DO SOMETHING THAT CAUSED MEGA CRASH LAST TIME – CAN IT BE AVOIDED
26.1K5 -
2:52
Hack
11 hours agoAn unusual idea with a bottle and a can of spray paint
24K6 -
25:18
Brewzle
1 day agoI Went Bourbon Hunting in a Tourist Trap | Hilton Head, SC
20.1K -
18:23
Freakin' Reviews
1 day agoKohl's Gadget Haul: Testing 6 Interesting Buys!
19.8K5 -
27:24
CarlCrusher
1 day agoUnexplained Skinwalker Encounter Reported at Nevada Ranch
16K5 -
2:33
Michael Heaver
1 day agoFarage’s Reform STUN UK
11.4K43 -
1:20:43
Crime Circus
17 hours agoInterrogation of Ex Cop ARRESTED for KlLLING his Neighbor - Shocking Police Interview!!
8.25K8