100 series convergence tests (no food, no water, no stop)

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How to do the series convergence tests for your Calculus 2 class. You will learn all types of convergence tests including direct comparison, telescoping series, limit comparison test, ratio test, root test, p-series, geometric series, and more! Best wishes for your calculus 2 class!

Check out my other "100-everything" series:

*mistakes*
Thanks to several viewers, at Q25, 1:53:40 , n should go from "2" to inf. And in that case, cos(pi*n) will produce 1,-1,1,-1,... but it is still a convergent alternating series.

Thanks to Chester, at 2:34:35, I meant to say 1/3 is less than "1", not 0. So we can draw a conclusion from the Ratio Test.

Thanks to Alberto! At 4:52:58 the final answer should be x is less than “-1”

Highlights: (see pinned comment for ALL timestamps)
start: 0:00
1, Classic proof that the series of 1/n diverges, 4:17
2, series of 1/ln(n) by The List, 11:10
3, series of 1/(ln(n^n)) by Integral Test, 17:05
4, Sum of 1/(ln(n))^ln(n) by Direct Comparison Test, 22:45
9, Sum of (-1)^n/sqrt(n+1) by Alternating Series Test, 49:10
15, Sum of n^n/(n!)^2 by Ratio Test, 1:22:20
16, Sum of n*sin(1/n) by Test for Divergence from The Limit, 1:28:04
26, Sum of (2n+1)^n/n^(2n) by Root Test, 1:58:11
30, Sum of n/2^n, 2:10:40
32, Sum of 1/n^(1+1/n), 2:22:30
41 to 49, true/false: 2:52:58
90, Sum of (-1)^n/n! = 1/e by Power Series, 5:24:40
100, Alternating Harmonic Series 1-1/2+1/3-1/4+1/5-... converges to ln(2) by Power Series, 5:54:40
101, Series of 3^n*n!/n^n by Ratio Test, 6:00:00

#100series #calculus #satisfying #apcalculus #gcse
May 6th, 2019
  1. blackpenredpen
  2. 100 series
  3. Series Convergence Tests
  4. series of 1/ln(n)
  5. sum of 1/(n*ln(n))
  6. calculus 2 series convergence tests
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Here you are! You can open a fitness centre and run a course : no food, no water, no stop!
More math, less fat hahaha~



Q1. Sum of 1/n, 4:17
Q2. Sum of 1/ln(n), 11:30
Q3. Sum of 1/ln(n^n), 17:23
Q4. Sum of 1/(ln(n))^ln(n), 23:00
Q5. Sum of (-1)^n/arctan(n), 32:04
Q6. Sum of 2^n/(3^n+n^3), 35:47
Q7. Sum of 3^n/(2^n+n^2), 39:01
Q8. Sum of n*sin^2(n)/(n^3+2), 46:17
Q9. Sum of (-1)^n/sqrt(n+1), 49:31
Q10. 1/2-1/3+2/9-4/27+... 55:31
Q11. Sum of (1/sqrt(n)-1/n), 58:21
Q12. Sum of 1/n^2ln(n), 1:03:28
Q13. Sum of 1/sqrt(n)e^sqrt(n), 1:06:54
Q14. Sum of n^n/3^n^2, 1:19:03
Q15. Sum of n^n/(n!)^2, 1:22:06
Q16. Sum of nsin(1/n), 1:28:05
Q17. Sum of 1/(n+3^n), 1:32:09
Q18. Sum of sin(2n)/(n+3^n), 1:34:02
Q19. Sum of n((-1)^n)/(3n+1), 1:36:27
Q20. 1/2+1/6+1/12+1/20... 1:38:28
Q21. Sum of (n!)/e^(n^2), 1:42:52
Q22. Sum of (n^2 + 1)/(n^3 +1), 1:46:35
Q23. Sum of sin(1/n^2), 1:48:59
Q24. Sum of cos^2(1/n), 1:51:51
Q25. Sum of cos(pi x n)/ln(n), 1:53:33
Q26. Sum of (2n + 1)^n / [n^(2n)], 1:58:09
Q27. Sum of 1/2^[ln(n)], 2:00:35
Q28. Sum of 1/3^[ln(n)], 2:03:23
Q29. Sum of (3n^2 + n)/sqrt(n^5 + 2n + 1), 2:04:16
Q30. Sum of n/(2^n), 2:10:41
Q31. Sum of (n!)^2 / (2n)!, 2:17:43
Q32. Sum of 1 / [n^(1+1/n), 2:21:55
Q33. Sum of 1 / [n^(1 + 1/n^2)], 2:26:40
Q34. Sum of 1, 2:30:10
Q35. Sum of n^2 / (2^n + 3^n), 2:30:58
Q36. Sum of (1 – 1/n)^n, 2:35:19
Q37. Sum of (1 – 1/n)^(n^2), 2:36:45
Q38. Sum of 1 / sin^4(n), 2:40:25
Q39. Sum of (n!)/(n^n), 2:41:45
Q40. Sum of 1/(n^3 + 3n^2 + 2n), 2:45:56
Q41. If sum of (an)^2 converges, then sum of an also converge, 2:52:52
Q42. If sum of an converges, then sum of (an)^2 also converges, 2:54:09
Q43. If sum of an converges, then sum of 1/(an) must diverge, 2:55:48
Q44. If sum of an diverges, then sum of 1/an must converge, 2:57:16
Q45. If sum of an converges, then sum of (an)/n must also converge, 2:58:40
Q46. If sum of an and sum of bn both converge, then sum of (an + bn) must converge, 3:00:10
Q47. If sum of an and sum of bn both diverge, then sum of (an – bn) must diverge, 3:01:41
Q48. If sum of an and sum of bn both diverge, then sum of (an x bn) must diverge, 3:03:55
Q49. If sum of an and sum of bn both converge, then sum of (an x bn) must converge, 3:05:57
Q50. Sum of 0, 3:08:15
Q51. Sum of n x sqrt[sin(1/n^2)], 3:08:52
Q52. Sum of [1 – sin(1/n)], 3:12:16
Q53. Sum of [1 – cos(1/n)], 3:18:05
Q54. Sum of 1 / cubert(2^n + 1), 3:22:51
Q55. Sum of 1/[sqrt(n) x ln(n)], 3:25:49
Q56. Sum of (n – 1)/sqrt(n^3 + 2n + 5), 3:26:32
Q57. Sum of [n^2 x 2^(n+2)] / 4^n, 3:32:00
Q58. Sum of [(nth root of 2) – 1], 3:36:55
Q59. Sum of [(nth root of 2) – 1]^n, 3:41:30
Q60. Evaluate sum of an, where a1 = 9 and an = (6 – n) x an-1, 3:43:23
Q61. Sum of [(n!)^n] / [n^(10n)], 3:46:23
Q62. Sum of [(2n)!] / n^n, 3:48:14
Q63. Sum of e^(-n) x sin n, 3:52:46
Q64. Sum of [tan(1/n)] / n^2, 3:56:58
Q65. Sum of (n^10 x 4^n) / n!, 4:01:53
Q66. Sum of (2^n x n!) / (n + 2)!, 4:04:58
Q67. Sum of 1 / sqrt(n!), 4:09:13
Q68. Sum of 1 / ln(n!), 4:11:24
Q69. Sum of [n(n+2)] / (2n+1)^2, 4:15:33
Q70. Sum of [e^(1/n) – e^(1/(n+2))], 4:16:57
Q71. Sum of (ln n) / n^2, 4:21:15
Q72. Sum of n^3 / (2n^5 + 3n – 4), 4:23:32
Q73. Sum of [(1-2n)/(3+4n)]^n, 4:24:54
Q74. Sum of (e^n) / [2^(2n-1)], 4:27:28
Q75. Sum of (n^3 – 2n – 1) / (2n^5 + 3n – 4), 4:30:02
Q76. Sum of 1 / (n + sqrt(n)), 4:33:12
Q77. Sum of 1 / (n x sqrt(n)), 4:35:15
Q78. Sum of sqrt(cos(1/n)), 4:36:10
Q79. Sum of (3^n x n^2) / n!, 4:37:45
Q80. Sum of n / (2^n), 4:41:09
Q81. Values of x for 1^x + 2^x + 3^x + ... + n^x + ... converge, 4:51:19
Q82. Values of x for x^1 + x^2 + x^3 + ... + x^n + ... converge, 4:53:08
Q83. Values of x for sum of (x - 2)^n / n^n converge, 4:54:39
Q84. Values of x for sum of (x^n) / n converge, 4:58:43
Q85. Values of x for sum of (x – 1)^n / (n x 3^n) converge, 5:04:18
Q86. Values of x for sum of (n!) x^n converge, 5:09:00
Q87. Values of x for sum of 1 / [x(ln x)^k] converge, 5:12:24
Q88. Values of x for sum of [1/(1 – x)]^n converge, 5:15:44
Q89. Values of x for sum of (sum of x^m)^n converge, 5:19:35
Q90. Sum of [(-1)^n] / (n!), 5:24:28
Q91. Sum of (pi/2 – arctan n), 5:25:34
Q92. Sum of sin^2 (1/n), 5:29:49
Q93. Sum of 1 / [sqrt n – sqrt(n+1)], 5:32:52
Q94. Sum of [1/sqrt n – 1/sqrt(n+1)], 5:35:55
Q95. Sum of 1 / e^(sqrt n), 5:38:16
Q96. Sum of 1 / [n x sqrt(n^5 – 1)], 5:43:35
Q97. Sum of ln[n/(n+2)], 5:46:12
Q98. Sum of 1/(e^n + 1), 5:49:23
Q99. Sum of 1/ln(e^n – 1), 5:50:42
Q100. 1 – 1/2 + 1/3 – 1/4 + 1/5 – 1/6 + ..., 5:54:20
Q101. Sum of (3^n x n!) / (n^n), 6:00:25

VibingMath
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School bell: *rings*

Teacher: Let me just say one more thing.
Teacher:

ceddy
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so, what do you eat in the morning ?
me : a bowl of cereals
this guy : a bowl of serials

dancibotaru
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That’s a lot of effort bro, those are the people who should be supported ❤

bakrkhabbaz
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The real talent isn't the math part, it is how he held that microphone for 6 hours easily.

razerglitch
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Me:**Is absent for one day**


The teacher:

RoccoArgubright
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I did about 15 of these with my friends in 7th grade, and I was SO TIRED. How you did this without dropping dead is awesome. subbed

johnvonneumannsdaddy
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Her: he's probably cheating on me with other girls.
Him:

paroxysmal
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Imagine forgetting to press the record button

maggutv
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trying to find my homework problem solution in this 6 hour video

mapengbo
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I just watched this during my review for my Calc 2 finals. I understood the how the tests work and how and to what situations they are used through this video more than the notes and lectures in our online zoom classes. Thank you very much. It also was really fun while watching! I hope to see more of this in the future :D

이하나-ckq
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Do it for 3 years daily and you'll become One Integral Man.

SanNico
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Time stamps for you guys!
Q1. Sum of 1/n, 4:17
Q2. Sum of 1/ln(n), 11:30
Q3. Sum of 1/ln(n^n), 17:23
Q4. Sum of 1/(ln(n))^ln(n), 23:00
Q5. Sum of (-1)^n/arctan(n), 32:04
Q6. Sum of 2^n/(3^n+n^3), 35:47
Q7. Sum of 3^n/(2^n+n^2), 39:01
Q8. Sum of n*sin^2(n)/(n^3+2), 46:17
Q9. Sum of (-1)^n/sqrt(n+1), 49:31
Q10. 1/2-1/3+2/9-4/27+... 55:31


Q10 to Q20. Thanks to "WHY IT"
Q11. Sum of (1/sqrt(n)-1/n), 58:21
Q12. Sum of 1/n^2ln(n), 1:03:28
Q13. Sum of 1/sqrt(n)e^sqrt(n), 1:06:54
Q14. Sum of n^n/3^n^2, 1:19:03
Q15. Sum of n^n/(n!)^2, 1:22:06
Q16. Sum of nsin(1/n), 1:28:05
Q17. Sum of 1/(n+3^n), 1:32:09
Q18. Sum of sin(2n)/(n+3^n), 1:34:02
Q19. Sum of n((-1)^n)/(3n+1), 1:36:27
Q20. 1/2+1/6+1/12+1/20... 1:38:28

*HELP ME WITH THE REST! THANK YOU* (I will credit you in my pinned comment)

blackpenredpen
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03:45:48 limit conv. against 585. Thank you so much for your effort ❤

redweg
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Someone: What do you watch on YouTube?
Me: It’s complicated

erdfgdvrefdvewdghebs
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Dude - you are amazing. I have a tremendous amount of respect for you, especially because I just recently started tutoring students in math (all high school math, undergraduate statistics, and now undergraduate calculus). But my god, man, why would you deprive yourself of food/water for six hours?! My throat hurts just thinking about how much talking is involved in this video!

covariance
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Just wanted to thank you. Anyone learning math needs to watch you. I've watched so many videos, and was still confused. It wasn't till I found your channel that I understood. Math makes sense!

bjpickens
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He doesn't love math
Math loves him

spiderjerusalem
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Calc-man💪
Also: 6 hours video 6 ads
Other youtubers: 10 min video infinite ads!

amirparsi
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I don't understand how i get exhausted after a one hour lecture in my college but left out more energetic after watching this video...Thank you so much for this .

naren