This video is a compilation of eight shorter videos I have created showing dissection proofs for infinite geometric series with ratio of the form 1/n and first term 1/n. To see the original videos (in shorter form and typically with more dramatic music), check the links below. When you have seen enough of these dissections, you should be able to guess the general formula for such a geometric series (and perhaps the more general form, which can be found in other videos on my channel).
Here are the original series videos (along with attribution; for more detailed attribution, see the original videos):
r = 1/2: • Geometric series: sum of powers of 1/2 (vi... (attribution: Roger B. Nelsen)
r = 1/3: • Geometric series: sum of powers of 1/3 II ... (attribution: Rick Mabry)
r = 1/4: • Geometric series: sum of powers of 1/4 (vi... (attribution: Rick Mabry)
r = 1/5: • Geometric series: sum of powers of 1/5 II ... (attribution: Rick Mabry)
r = 1/6: • Geometric Series: sum of powers of 1/6 (vi... (attribution: James Tanton)
r = 1/7: • Geometric series: sum of Powers of 1/7 (vi... (attribution: James Tanton)
r = 1/8: • Geometric Series: sum of powers of 1/8 (vi... (attribution: Roger B. Nelsen)
r = 1/9: • Geometric Series: sum of powers of 1/9 (vi...
If you like series dissections, check out my playlists:
• Geometric Sums
• Infinite Series
To learn more about animating with manim, check out:
https://manim.community
___________________________________
Music:
Adrift Among Infinite Stars by Scott Buckley | / scottbuckley
Music promoted by https://www.free-stock-music.com
Attribution 4.0 International (CC BY 4.0)
https://creativecommons.org/licenses/...
Поделиться в:
Доступные форматы для скачивания:
Скачать видео mp4
Информация по загрузке:
Скачать аудио mp3
Похожие видео
array(10) {
[0]=>
object(stdClass)#6028 (5) {
["video_id"]=>
int(9999999)
["related_video_id"]=>
string(11) "ocbI2R13Jxw"
["related_video_title"]=>
string(53) "Sum of Squares Visual Proofs: From Level 1 to Level 5"
["posted_time"]=>
string(19) "1 год назад"
["channelName"]=>
string(26) "Mathematical Visual Proofs"
}
[1]=>
object(stdClass)#6001 (5) {
["video_id"]=>
int(9999999)
["related_video_id"]=>
string(11) "C-TsuHseZkg"
["related_video_title"]=>
string(168) "ПРЕМЬЕРА СВЕЖЕГО ДЕТЕКТИВА 2025 ИЗ ФРАНЦУЗСКОЙ КОЛЛЕКЦИИ "УБИЙСТВА В..."!Убийство в Гильвинеке"
["posted_time"]=>
string(21) "1 день назад"
["channelName"]=>
string(10) "Filmegator"
}
[2]=>
object(stdClass)#6026 (5) {
["video_id"]=>
int(9999999)
["related_video_id"]=>
string(11) "VwMFTRhiCvY"
["related_video_title"]=>
string(175) "ОСЕЧКИН: "Достанут всех, вот что происходит": кто "засветился" в ФСБ, почему Шлосберг, ФРОНТ, ОБМЕН"
["posted_time"]=>
string(24) "12 часов назад"
["channelName"]=>
string(24) "И Грянул Грэм"
}
[3]=>
object(stdClass)#6033 (5) {
["video_id"]=>
int(9999999)
["related_video_id"]=>
string(11) "o1eLKODSCqw"
["related_video_title"]=>
string(38) "A New Way to Look at Fibonacci Numbers"
["posted_time"]=>
string(19) "5 лет назад"
["channelName"]=>
string(12) "Jacob Yatsko"
}
[4]=>
object(stdClass)#6012 (5) {
["video_id"]=>
int(9999999)
["related_video_id"]=>
string(11) "eHbtc50-qXo"
["related_video_title"]=>
string(62) "A Dozen Proofs: Sum of Integers Formula (visual proofs) #SoME2"
["posted_time"]=>
string(21) "2 года назад"
["channelName"]=>
string(26) "Mathematical Visual Proofs"
}
[5]=>
object(stdClass)#6030 (5) {
["video_id"]=>
int(9999999)
["related_video_id"]=>
string(11) "XXzhqStLG-4"
["related_video_title"]=>
string(39) "Putting Algebraic Curves in Perspective"
["posted_time"]=>
string(19) "5 лет назад"
["channelName"]=>
string(13) "Bill Shillito"
}
[6]=>
object(stdClass)#6025 (5) {
["video_id"]=>
int(9999999)
["related_video_id"]=>
string(11) "vJ_K3Elnyus"
["related_video_title"]=>
string(99) "Proof without words : Geometric Proof of Arc Tangent Derivative | #manim #geometry #calculus #maths"
["posted_time"]=>
string(27) "6 месяцев назад"
["channelName"]=>
string(15) "Maths With Buka"
}
[7]=>
object(stdClass)#6035 (5) {
["video_id"]=>
int(9999999)
["related_video_id"]=>
string(11) "p6j2nZKwf20"
["related_video_title"]=>
string(100) "Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]"
["posted_time"]=>
string(21) "2 года назад"
["channelName"]=>
string(14) "polymathematic"
}
[8]=>
object(stdClass)#6011 (5) {
["video_id"]=>
int(9999999)
["related_video_id"]=>
string(11) "4KlvI_uK9zs"
["related_video_title"]=>
string(45) "Complex Numbers Have More Uses Than You Think"
["posted_time"]=>
string(21) "2 года назад"
["channelName"]=>
string(11) "Morphocular"
}
[9]=>
object(stdClass)#6029 (5) {
["video_id"]=>
int(9999999)
["related_video_id"]=>
string(11) "SBOqFdEfIIA"
["related_video_title"]=>
string(66) "Шапито в пальто | Уральские пельмени"
["posted_time"]=>
string(24) "14 часов назад"
["channelName"]=>
string(36) "Лучшие вечерние шоу"
}
}
![Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]](https://ricktube.ru/thumbnail/p6j2nZKwf20/mqdefault.jpg)
